You'll Die at Midnight (1986)

Original title: Morirai a mezzanotte

Nicola, a cop, spies on his wife Sarah buying sexy black panties and realises that she is having an affair. Following a violent confrontation, he leaves her. Immediately after, whilst taking a shower, Sarah is stabbed to death with an icepick. Believing it to be an simple crime of passion, the police assign Inspector Pierro Terzi to bring his former colleague in. But Professor Anna Berardi, a criminal pyschologist who is friends with both men, believes the Nicola is innocent. She suggests that the real killer is Franco Tribbo, a maniac known as "The Midnight Killer" who supposedly died in a hospital fire several years previously. Terzi is not conviced but Nicola is killed and the murders continue...