A killer stalking the streets of Montmartre has murdered five women and Maigret is making no head-way in the case. After consulting the distinguished psychiatrist, Professor Tissot, he decides to use psycho-logical means to trap the killer. Firstly, he fakes an arrest, hoping that the murderer, in a fit of jealousy at someone stealing his thunder, will strike again. And he provides him with scores of suit-able potential victims in the shape of policewomen, proficient in the art of judo. The trap has been set.