09/30/2012 at 01:20 PM EDT
Arnold Schwarzenegger says his affair with his family's housekeeper wasn't the first time he cheated on Maria Shriver
The action star and former California governor admits in his new autobiography to a "hot affair" with actress Brigitte Nielsen while they filmed Red Sonja
in 1985 when he and Shriver were living together, Time magazine reports.
Schwarzenegger, now 65, never thought the relationship with Nielsen was serious and that the fling only convinced him to marry Shriver, he writes in Total Recall: My Unbelievably True Life Story,
according to Time.
Nielsen, now 49, wrote in her own autobiography last year about an "outrageous affair" with Schwarzenegger but said she didn't know he was with Shriver at the time.
Shriver filed for divorce
in 2011 after Schwarzenegger revealed his affair
with Mildred Baena which produced a son, Joseph, now a teenager.