The Fifth Cord (1971)

After a high-class party in Rome, there's an assault. The victim is injured but lives. Andrea, an investigative reporter who drinks too much, is assigned the story. Then, always on Tuesdays, there are a series of murders. At each crime scene, a glove is left with a finger cut off for each victim. After four murders, Andrea thinks he's making progress, but by this time he may himself be a suspect, and someone he loves is in danger.