The Case Against X: Paul Dorgères, a wealthy industrialist, has been mysteriously murdered. The investigation is entrusted to the experienced Chief Inspector Bonnardel and his young rookie assistant, Inspector Richard. Suspicion turns to his mistress Catherine Villard, with whom he had just broken up on the night of the crime. She is soon arrested and charged. However, Inspector Richard discovers a button at the scene of the crime which could help him to trace the trail and confound the culprit(s).