With Cain go wander through shades of night, And never show thy head by day nor light (5.6.6).
At the end of the play, when Henry finds out that Exton has killed Richard (on Henry's behalf), he banishes the guy and compares him to Cain (who killed his brother Abel in the Bible). What's weird about this is how Henry refuses to acknowledge that he is the one who caused his cousin Richard's death. If anything, Henry is like Cain, so it seems unjust that Exton should be banished.
This scene also reminds us of how and why Richard banished Henry back in Act 1, Scene 3. (Remember, when Henry publicly accused Mowbray of murdering Gloucester, he was really accusing Richard without coming out and saying so. Richard responded by throwing Henry and Mowbray out of the country.) Is Henry's banishment of Exton really any different than Richard's banishment of Henry and Mowbray?