This Bible contradiction is from the Skeptic's Annotated Bible.
A man may divorce his wife if he finds some uncleanness in her. (Or if she no longer has favor in his eyes.)
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.
A man may divorce his wife only if she has fornicated.
Matthew 5:32 View context
Whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery.
Matthew 19:9 View context
Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery.
Divorce is permitted if an unbelieving spouse 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.
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
Whosoever shall put away his wife, and marry another, committeth adultery.
Luke 16:18 View context
Whosoever putteth away his wife and marrieth another, committeth adultery