On a train departing the nation’s capital, tennis champion Guy Haines (Granger) meets a wealthy young admirer, Bruno Antony (Walker), who seems to know a lot about his unhappy marriage to clingy Miriam (Elliott). As they converse, Bruno reveals that he despises his overbearing father (Hale), and proposes — theoretically — an “exchange murder.” Guy laughs off the suggestion. But soon after they reach their end destination, Miriam turns up dead, strangled by an unknown assailant…