Schwarzenegger has admitted to reducing the sentence of a political ally's son as a personal favor. On Monday, the State Assembly approved a bill that would require a governor to notify the crime victim's family and the district attorney involved in a case before they could commute any sentence.
Those parties would be given at least 30 days to petition the governor before a clemency decision is made.
The bill by Assemblyman Marty Block, a Democrat from San Diego, passed 61-0 and heads to the Senate.
Republican Assemblyman Allan Mansoor of Costa Mesa drafted a similar constitutional amendment. His office says Block's bill is not restrictive enough.
The Associated Press contributed to this story