A former companion forced his way into a home in Río Claro early Sunday, chased his ex-girlfriend into the bathroom where he shot her twice in the head.
Then he tried to kill the new man in her life but missed.
The gunman, identified with the last name of Calvo drove to a nearby bridge and hung himself, said the Judicial Investigating Organization. He was 53.
The dead woman was identified by the last name of Kraemer. She was 43, agents said.
Investigators said that the couple had a 7-year-old child, but it was not immediately made clear if the child also was in the house where the shooting took place.
They had separated some months ago, investigators said.