Amateur tennis star Guy Haines wants to divorce his vulgar, promiscuous wife Miriam so he can marry the elegant Anne Morton, the daughter of a US Senator. On a train, Haines meets a smooth-talking psychopath, Bruno Antony, who tells him about his idea for a murder scheme: two perfect strangers meet and "swap murders" ? Bruno suggests he kill Miriam and Guy kill Bruno's hated father. Each will kill a total stranger with no apparent motive, so neither will be suspected.