When celebrated stage star Arlena Marshall (Diana Rigg) is found murdered on a luxurious island, the exasperating but brilliant Poirot is called upon to find the culprit. Given Marshall's propensity for making enemies, the question isn't "Who wanted to see her dead?" but "Who didn't?" Suspects include biographer Rex Brewster (Roddy McDowall) aggrieved theatrical producers Odell and Myra Gardener (James Mason and Sylvia Mill) and Arlena's husband, Kenneth.