A woman is found dead on a train, the name "Rex" written on the pull-down blind. It is the third in a mysterious string of murders. Later, while detective novelist Paul Temple, his wife Steve, and Scotland Yard's Sir Graham Forbes are at a nightclub, they receive a message from singer Norma Rice concerning the "Rex" murders. But before Sir Graham has the chance to speak to her, she drops dead in the middle of her act... Can Paul solve the case before "Rex" strikes again?