A woman is found dead on a train, and the name "Rex" has been written on the pull-down blind. It is the third in a mysterious string of "Rex" murders, all carried out on trains. And soon there's a fourth murder. All the victims are discovered to have been the wealthy patients of a doctor who specialises in nervous disorders.
The detective novelist Paul Temple and his wife Steve are called in to help Scotland Yard's Sir Graham Forbes solve the case before the serial killer strikes again. While at a nightclub, they receive a message from singer Norma Rice concerning the murders. But before Sir Graham has the chance to speak to her she dies, falling down the stairs in the middle of her second number, What's Cooking in Cabaret?.
The suspects include the Egyptian therapist Dr Kohima, his mysterious secretary Mrs Trevelyan, and a salesman, Hugh Pryse of the Quick Boil Kettle Company (in the next carriage when one of the murders takes place).
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