Clearly, however he took this personally and held a personal vendetta against Michael for it, DESPITE the fact that Green's assassination was strictly business.
The circumstances of Greene's death in the book and the movie are somewhat different. In the movie, Greene is only killed when Barzini and the others are. I've always thought that Greene made a critical mistake in the movie version when he told Michael that "I tocked to Barzini. I can make the deal with him and still keep my hotel." Because of this remark, when Michael learns from Vito that Barzini and the other heads of the Five Families will try to kill him, he has reason to believe that Greene is in on this and that part of "the deal" is Michael being dead. Therefore, he has reason to consider Greene himself a deadly enemy who should be eliminated along with the others--after all, Greene was (in the novel) said to have been a member of the assassination squad "Murder Inc." He was hardly a slouch himself when it came to violence.
