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In Paul's epistle it states:
"To the married I give charge, not I but the Lord, that the wife should not separate from her husband ... and that the husband should not divorce his wife. To the rest I say, not the Lord, ... But if the unbelieving partner desires to separate, let it be so; in such a case the brother or sister is not bound. For God has called us to peace." (1 Corinthians 7:10-15 RSV)
The first section, "not I but the Lord", roughly matches Jesus' teaching on divorce, found in an antithesis (Matthew 5:32) with parallels in Matthew 19:9, Luke 16:18, and Mark 10:11. The second section, "I say, not the Lord", gives Paul's own teaching on divorce.
In the Catholic Church and in some Protestant denominations (although most Protestants allow divorce in all circumstances), this is interpreted as allowing the dissolution of a marriage between two non-baptized persons in the case that one (but not both) of the partners seeks baptism and converts to Christianity and the other partner leaves the marriage. According to the Catholic Church's canon law, the Pauline Privilege does not apply when either of the partners was a Christian at the time of marriage. It differs from annulment because it dissolves a valid natural (but not sacramental) marriage whereas an annulment declares that a marriage was invalid from the beginning.
The Petrine Privilege (allowing remarriage after divorce) may be invoked if only one of the partners was baptized at the time of the second marriage, despite the fact that Paul does not himself comment on the lawfulness of such a remarriage.