It firmly believes, professes, and proclaims that those not living within the Catholic Church, not only pagans, but also Jews and heretics and schismatics cannot become participants in eternal life, but will depart “into everlasting fire which was prepared for the devil and his angels” (Mt 25:41), unless before the end of life the same have been added to the flock; and that the unity of the ecclesiastical body is so strong that only to those remaining in it are the sacraments of the Church of benefit for salvation, and do fasting, almsgiving, and other functions of piety and exercises of Christian service produce eternal reward, and that no one, whatever almsgiving he has practiced, even if he has shed blood for the name of Christ, can be saved, unless he has remained in the bosom and unity of the Catholic Church. (Denzinger-Hünermann 1351. Council of Florence, Decree on behalf of the Jacobites, February 4, 1442)

Canon 9: The members of the Church are not allowed to meet in the cemeteries, nor attend the so-called martyrs of any of the heretics, for prayer or service. […] Canon 34: No Christian shall forsake the martyrs of Christ, and turn to false martyrs, for they are aliens from God. Let those, therefore, who go after them, be anathema.  (Synod of Laodicea, Canons 9. 34)

Believe strongly and without a doubt, that any heretic or schismatic, baptized in the name of the Father and of the Son and of the Holy Spirit, absolutely cannot be saved if he is not a member of the Catholic Church, however generous his alms may be, and even if he sheds his blood for the name of Christ. For all those who do not remain in unity with the Church cannot attain salvation, despite being baptized, and despite their almsgiving, abundant though it may be, and even despite their suffering death for the name of Christ, if they persists in the error, whether heretical or schismatic, which leads to death.  (Saint Fulgentius of Ruspe. Letter to Peter on the Faith, Ch.39, no. 80 – ML 65, 704)

Do they deem that they have Christ with them when they are collected together, who are gathered together outside the Church of Christ? Even if such men were slain in confession of the Name, that stain is not even washed away by blood: the inexpiable and grave fault of discord is not even purged by suffering. He cannot be a martyr who is not in the Church; he cannot attain unto the kingdom who forsakes that which shall reign there. Christ gave us peace; He bade us be in agreement, and of one mind. He charged the bonds of love and charity to be kept uncorrupted and inviolate; he cannot show himself a martyr who has not maintained brotherly love. (Saint Cyprian of Carthage, On the Unity of the Church, I, no. 13-14 – ML 4, 510-511)

 They cannot dwell with God who would not be of one mind in God’s Church. Although they burn, given up to flames and fires, or lay down their lives, thrown to the wild beasts, that will not be the crown of faith, but the punishment of perfidy; nor will it be the glorious ending of religious valor, but the destruction of despair. Such a one may be slain; crowned he cannot be. He professes himself to be a Christian in such a way as the devil often feigns himself to be Christ, as the Lord Himself forewarns us, and says, “Many shall come in my name, saying, I am Christ, and shall deceive many” (Mk 13:16). As he is not Christ, although he deceives in respect of the name; so neither can he appear as a Christian who does not abide in the truth of Hi s Gospel and of faith.(Saint Cyprian of Carthage. On the Unity of the Church, I, no.14 – ML 4, 510-511)

Can the power of baptism be greater or of more avail than confession, than suffering, when one confesses Christ before men and is baptized in his own blood? And yet even this baptism does not benefit a heretic, although he has confessed Christ, and been put to death outside the Church, unless the patrons and advocates of heretics declare that the heretics who are slain in a false confession of Christ are martyrs, and assign to them the glory and the crown of martyrdom contrary to the testimony of the apostle, who says that it will profit them nothing although they were burnt and slain. (1Cor 13:3)  (Saint Cyprian of Carthage, Epistle LXXII to Jubaianus, no. 21)

I have proved countless times, both by debate and by writing, that they cannot have the death of martyrs because they have not the life of Christians, since it is not the pain but the purpose that makes a martyr.  (Saint Augustine, Letter 204: to Dulcitius, no. 4)

 With good reason you might say these things, seeking the glory of the martyrs, if you had the cause of the martyrs. The Lord did not call happy those who suffer such things, but rather happy those who suffer them for the sake of the Son of Man, who is Jesus Christ. However, you did not suffer for him, but against him. You suffer, it is true, but because you do not believe in him, and so you suffer for your disbelief. How, then, do you presume to have the faith that Jesus Christ left to the apostles? Do you wish, by chance, that men were so blind and so deaf as to not read or hear the Gospel, in which they discover that which Christ left for his apostles to believe regarding his Church? And if you divide and separate yourselves from it, you actually rebel against the words of the head and the body, and nonetheless you presume to suffer persecution for the Son of Man and for the faith that he left to the Apostles. […] This is, then, the faith regarding the Holy Church that he left to the disciples. It is this faith, Donatists, that you oppose with your resistance. And you insist that you suffer persecution for the faith that Christ the Lord left to his Apostles! With surprising insolence and blindness you contradict this Son of Man, who recommended his Church which was in its beginnings in Jerusalem, and producing fruit and spreading to all peoples, and you proclaim that you are suffering calamities for the sake of the Son of Man.  (Saint Augustine, Contra Gaudentium Donatistarum Episcopum, lib. I, c.20/n.22)

In the next place, if all who are killed are baptized in their own blood, then all robbers, all unrighteous, impious, accursed men, who are put to death by the sentence of the law, are to be considered martyrs, because they are baptized in their own blood. But if only those are baptized in their own blood who are put to death for righteousness’ sake, since theirs is the kingdom of heaven, (Mt 5:10) you have already seen that the first question is why you suffer, and only afterwards should we ask what you suffer. Why therefore do you puff out your cheeks before you have shown the righteousness of your deeds? Why, does your tongue resound before your character is approved? If you have made a schism, you are impious; if you are impious, you die as one guilty of sacrilege, when you are punished for impiety; if you die as one guilty of sacrilege, how are you baptized in your blood? Or do you say, I have not made a schism? Let us then inquire into this. Why do you make an outcry before you prove your case?  (Saint Augustine. Answer to Petilian the Donatist, Book I, ch.23/52)

 But since there are many that suffer this, be it due to their own sins, or due to their crimes, one must be attentive in distinguishing not so much the hardship suffered, but the cause. A criminal could receive a chastisement similar to that of a martyr, but the cause is different. Three were crucified: one was the Savior, the second was saved, and the third, condemned. The suffering was the same for all three, but the cause was far different. […] Suffering is the same for the good and the evil. That is why what makes martyrs is not the suffering, but the cause. If it were merely suffering that made martyrs, all mines would be full of martyrs, all chains would bind martyrs, all of those wounded by the sword would be crowned. Therefore, let us carefully discern the cause. May no one say: I am just, for I suffer.  (Saint Augustine. Ennaratio in Psalmum 34/2, n.1, 13)

But true martyrs are such as those of whom the Lord says, “Blessed are they which are persecuted for righteousness’ sake.” (Mt 5:1). It is not, therefore, those who suffer persecution for their unrighteousness, and for the divisions which they impiously introduce into Christian unity, but those who suffer for righteousness’ sake.  (Saint Augustine. Letter 185, ch.2, n. 9)

Adulterers, bandits, assailants, murderers, and all criminals suffer many torments; I, your martyr, also suffer countless torments, but “distinguish my cause from the nation that is not holy” (Ps 42: 1). They may suffer what I suffer, but they do not have the same cause. In the furnace, I am purified, they are reduced to ashes. The heretics also suffer such things, many times through their own doing, wishing to be taken as martyrs. But against them have we sung: Defend my cause against all ungodly people. It is not the suffering which makes the martyr, but the cause.  (Saint Augustine. Sermon 327, n.1)

And martyrdom to avoid schism is no less glorious than martyrdom to avoid idolatry. Nay, it is to my mind greater. In one case a man is a martyr for his own single soul’s sake. But this is for the whole Church. Even now wast thou to persuade or constrain the brethren to come to one mind, thy true deed were greater than thy fall. This will not be reckoned to thee, the other will be lauded. And if thou shouldest be powerless to sway disobedient spirits, save, save thine own soul.  (Saint Dionysius of Alexandria. Letter To Novatian in: Eusebius of Cesarea, Historia Ecclesiastica, lib. III, c. 45) [Novation was killed during the reign of the Emperor Valerian I (253-260) – and never considered a martyr by the Church].

But, moreover, although Novatian did endure some suffering, yet was he not also slain. And although he was slain, yet was he not crowned. Why not? He was without the peace of the Church, without the bounds of concord, without the pale of that mother, of whom he ought to be a part who is a Martyr. Hear the Apostle, and though I have all faith, so that I could remove mountains, and have not charity, I am nothing. And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing. But Cyprian suffered, in concord with all, in the common peace of all, amid a company of Confessors; and, having often been a Confessor in reiterated persecutions, and harassed with many a torment, had at last given him to drink of the cup of salvation. This was to be crowned! Wherefore let Novatian have his Epistles to himself, to himself his haughtiness, to himself his pride, by which, whilst he is lifted up on high, he is dashed down to pieces, whilst he spares no one, he is himself cast out.  (Saint Pacian of Barcelona. Epistola II ad Simpronianum, n.VII,7 – ML 13, 1062-1063)

 The Marcionites and other heretics gloried in the multitude of their martyrs. as Sulpicius Severus of the Priscillianists wrote. (Sacr. Histor. lib. II, c.51, n.7) The heretics of our days imitate them. […] Even if we admitted that there exists schism without heresy, one who dies in schism may not be numbered among the martyrs, for he who is separated from the Catholic Church has no life. […] Consequently, among the schismatics, no martyrs exist. […] A heretic dies either due to his heresy, or due to an article of the Catholic Faith. In the first case he may not be considered a martyr, for, in dying, he is a sure testimony of his own diabolical persistence in error. […] The same we may say of a heretic who dies for one article of the true Faith; even though we admit that he died for one truth, he did not accept death for all of the truths proposed within the Faith, since he himself lacks faith. The theologians, led by Saint Thomas (SummaTheologica II-IIae, q. 5, a.3), teach that he who merely dies for one article of truth may not be considered a martyr, since he lacks both living as well as lifeless faith. However, when it is a heretic invincibiliter [i.e. in invincible ignorance] and ready to believe in any proposal of legitimate authority, he may be considered a martyr before God (coram Deo), but not before the Church (coram Ecclesia).
The norms of ‘De Servorum Dei beatifatione…’ were in use during almost two centuries within in the Sacred Congregation of Rites and were substantially passed on to the ‘Codex Iuris Canonici’ of 1917, according to the Apostolic Constitution ‘Divinus Perfectionis magister’ of John Paul II. (Benedict XIV. De Servorum Dei beatificatione et Beatorum canonizatione (syn.), lib.III, c. 20)

 Neither living nor lifeless faith remains in a heretic who disbelieves one article of faith. […] if, of the things taught by the Church, he holds what he chooses to hold, and rejects what he chooses to reject, he no longer adheres to the teaching of the Church as to an infallible rule, but to his own will. […] A heretic does not hold the other articles of faith, about which he does not err, in the same way as one of the faithful does, namely by adhering simply to the Divine Truth, because in order to do so, a man needs the help of the habit of faith; but he holds the things that are of faith, by his own will and judgment.  (Saint Thomas Aquinas. Summa Theologica II-II q. 5, a. 3)

The Apostle Paul has said: After a first and second warning, break off contact with a heretic, realizing that such a person is perverted and sinful and stands self-condemned. (Titus 3:10-11). But though the doctrine which men hold be false and perverse, if they do not maintain it with passionate obstinacy, especially when they have not devised it by the rashness of their own presumption, but have accepted it from parents who had been misguided and had fallen into error, and if they are with anxiety seeking the truth, and are prepared to be set right when they have found it. […]. On this ground I wrote even to some of the chief of the Donatists, not indeed letters of communion, which on account of their perversity they have long ceased to receive from the undivided Catholic Church which is spread throughout the world, but letters of a private kind, such as we may send even to pagans. These letters, however, though they have sometimes read them, they have not been willing, or perhaps it is more probable, have not been able, to answer. In these cases, it seems to me that I have discharged the obligation laid on me by that love which the Holy Spirit teaches us to render, not only to our own, but to all.  (Saint Augustine. Letter 43, n.1)

For, it must be held by faith that outside the Apostolic Roman Church, no one can be saved; that this is the only ark of salvation; that he who shall not have entered therein will perish in the flood; but, on the other hand, it is necessary to hold for certain that they who labor in ignorance of the true religion, if this ignorance is invincible, are not stained by any guilt in this matter in the eyes of God. Now, in truth, who would arrogate so much to himself as to mark the limits of such an ignorance, because of the nature and variety of peoples, regions, innate dispositions, and of so many other things? For, in truth, when released from these corporeal chains “we shall see God as He is” (1Jn 3:2), we shall understand perfectly by how close and beautiful a bond divine mercy and justice are united; but, as long as we are on earth, weighed down by this mortal mass which blunts the soul, let us hold most firmly that, in accordance with Catholic teaching, there is “one God, one faith, one baptism” (Ep 4:5); it is unlawful to proceed further in inquiry.  (Denzinger-Hünermann 2805. Pius IX. Allocution Singulari quadam, December 9, 1854)

 The Church Fathers […] basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it (LG 14). This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church: Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience – those too may achieve eternal salvation (LG 16). “Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men (AG 7).  (Catechism of the Catholic Church, no. 846-848)