This Bible contradiction is from the Skeptic's Annotated Bible.
Divorce is never permissible.
Matthew 19:6 View context
Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder.
Mark 10:11 View context
And he saith unto them, Whosoever shall put away his wife, and marry another, committeth adultery against her.
Luke 16:18 View context
Whosoever putteth away his wife, and marrieth another, committeth adultery: and whosoever marrieth her that is put away from [her] husband committeth adultery.
Only when the wife is unfaithful
Matthew 5:32 View context
But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
Matthew 19:9 View context
And I say unto you, Whosoever shall put away his wife, except [it be] for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.
When the 'unbelieving' partner chooses to leave
1 Corinthians 7:15 View context
But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such [cases]: but God hath called us to peace.
When the husband is displeased with his wife
Deuteronomy 24:1-2 View context
When a man hath taken a wife, and married her, and it come to pass that she find no favour in his eyes, because he hath found some uncleanness in her: then let him write her a bill of divorcement, and give [it] in her hand, and send her out of his house.
And when she is departed out of his house, she may go and be another man's [wife].