This Bible contradiction is from the Skeptic's Annotated Bible.

Verses

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].