Back at the palace, Richard has taken the throne, but he's super paranoid.
Richard worries aloud that his glory might be too short as king. He points out that Prince Edward (the rightful heir to the throne) is still alive and is a threat to him.
Richard obviously wants Buckingham to make the young princes disappear – forever.
When it's clear that Buckingham isn't taking the hint, Richard declares, verbatim, "I wish the bastards dead!"
Buckingham hesitates, which ticks off Richard.
Buckingham quickly excuses himself, saying he needs a minute to think about whether it's OK to murder two innocent children.
Richard calls a page to bring him a man who will do anything, no matter how heinous, for money. The page knows just the man – Sir James Tyrrell.
Since Richard has now found a murderer and conspirator more useful to him than Buckingham, he declares Buckingham is out of his inner-circle. (And likely soon to be dead.)
Stanley, Earl of Derby then enters with the news that Dorset has fled to see Richmond. (Remember that Richmond is Stanley's stepson, so we don't really know whose side he's on.)
Richard doesn't fixate on this news. Instead, without hesitation, he calls Catesby to him and hatches yet another plot, this time to protect his hard-earned crown. Richard wants Catesby to start spreading a rumor that his wife Anne is very sick and likely to die soon. Meanwhile, he plans to imprison Anne.
Richard plans to get Clarence's kids out of the way too – just to be safe. He isn't worried about Clarence's dull-witted young son, and he'll marry Clarence's little daughter Margaret off to some unimportant loser, probably to prevent a nobleman from marrying her and then claiming himself heir to the crown.
Richard then reveals the worst part of his plan. Once the hired murderer snuffs out the two princes in the tower, only their sister will be left behind. Richard thinks it would be a good idea to marry her after he gets rid of Anne.
Richard reasons that he's already killed a bunch of people, so what's a few more?
Richard then meets with Tyrrell, who runs off to kill the young princes.
Buckingham reminds Richard that he promised to give him the earldom of Hereford for his loyal service.
Richard ignores him.
Richard warns Derby that if Derby's wife (mother to Richmond) sends any letters to Richmond, Derby will pay for it.
Richard's mind is already moving to what's ahead (which seems like war with Richmond).
Richard then talks about King Henry VI, who prophesied long ago that Richmond would one day be King of England. Richard notes that Henry must have been mistaken in leaving out the part of the prophecy where he, King Richard III, kills Richmond.
Richard recalls another prophecy warning him to fear Richmond.
Richard finally stops being distracted enough to tell Buckingham to leave him alone, as Buckingham has been whining on the sidelines this whole time.
Buckingham realizes that for all his evil deeds, he's being repaid just like the other men Richard turned on. Before he ends up like Hastings, Buckingham decides to flee to Brecknock, a mansion in Wales.