Bigger was always afraid of white society. It is not until he he commits his first crime against whites that he begins to loose his fear of white society. By killing Mary, Bigger begins to feel empowered. He sees this as an act of rebellion against a white society that has oppressed him since the day he was born.
The thought of what he had done, the awful horror of it...formed for him for the first time in his fear-ridden life a barrier of protection between him and a world he feared. He had murdered and had created a new life for himself. It was something that was all his own, and its was the first time in his life he had had anything that others could not take from him.
Instead of escape, Bigger sees his act of rebellion as a chance to take flight. He felt that this was a new beginning for him and that his life was in his hands and not controlled by the white elite. The last chapter is of course Bigger's fate. Although Bigger might have thought he was taking flight, his destiny lay only in the fate of a black man who has killed a white woman: the most unforgivable of crimes in the eyes of the white court.