Your anger at the aggressor will guarantee that he will continue this behavior. Your nurturing and positive teaching will make a difference in the child who has hurt someone else. A key point of turning around his behavior is talking with the child about alternative ways that he could have handled conflict. Expect denial from the child if you ask him to own up to his behavior when he is upset and angry. Children, like the rest of us, are not rational creatures when angry.
Anger throws reason out the window.
The research shows that cognitive distortions such as minimizing, justifying or rationalizing their destructive behavior has been associated with individuals with antisocial behavior. Their pain is so great and their defenses so practiced that they cannot see their own part in the conflict. Do not set up a situation of threat where the child will feel the need to go into his defenses. Give him a cool down period before talking to him. Give him a choice of the place where he wants to cool down.