He was nominated for the Academy Award for Best Film Editing for MASH (1970-directed by Robert Altman) and, with John C. Howard, for Blazing Saddles (1974-directed by Mel Brooks).
After assisting at Metro Goldwyn Mayer, he became the head of sound editing at Universal Studios, where he worked on Psycho (1960).
The following year he edited MASH (1970) with Altman, which was an anti-war comedy that became a phenomenal success while the U.S. was still fighting the Vietnam War.
[6] Other films edited by Greene include Blazing Saddles (1974), Fun with Dick and Jane (1977), American Hot Wax (1978), and Rocky II (1979).
[7][8] Very early in his editing career, Greene was nominated for the American Cinema Editors Eddie award for a 1962 episode of the television series It's a Man's World.