In "The Twilight Saga : New Moon" after an unfortunate incident at the Cullen's home, Edward decides it's in Bella's best interest if he and his family move away. He takes her into the forest near to her home, and tells her that it's time for he and his family to move away. When she offers to come with him, he says that he no longer wants her, as she is not good for him, and he is tired of pretending to be something he isn't - human. He tells her she will never see him again, and it will be as if he never existed.
He asks for one promise from her, that she not do anything stupid as it would break Charlie's heart. Ather home, he forges a note to Charlie to make sure he knows where Bella is, then he leaves planning never to return, then he gets hit by a bus.