While on a Mediterranean cruise, Poirot is asked to investigate the murder of one of the passengers, Mrs. Clapperton who is found stabbed in the chest in her stateroom. She was somewhat haughty and generally disliked by the other passengers. Her henpecked husband, Colonel Clapperton, was ashore for the entire day with two other passengers. General Forbes, who admits to having been in love with the dead woman when they knew each other many years before, says he was having a nap. Then there is Miss Ellie Henderson, who is attracted to Colonel Clapperton but whose wife is in the way of any possible relationship. With everyone having a reasonable alibi, it is left to Poirot to find the killer.