This isn't in the novel the way the movie shows it.
Dembo does kill Willy...but differently.
In the novel, Dembo shaves his head (to change identity because the cops were able to identify the living robber as 'Maxwell Dembo') and confronts Willy at his home and then in his car. In the movie, Max is mad that Willy left he and Jerry behind. IN THE NOVEL HOWEVER, Max is mad because he thinks Willy told the police his identity (Willy was the only other person who knew about the robbery). After calling him a rat, he shoots Willy in the knee and then again until he dies.
Dembo then takes Willy's dead body off road and pisses on his corpse. BRUTAL.
I kinda like the movie's way better. GIMMIE A BIG BEAR HUG! *BANG*