And then there were none (1945)

http://www.imdb.com/title/tt0037515/

Directed by: René Clair

Writer: Agatha Christie (novel)
Dudley Nichols (screenplay)

Based on the novel by Agatha Christie of the same name. Ten people, all accused of murder, are guests of the mysterious Mr. and Mrs. U.N. Owen, whom none of the ten has ever actually met. One by one they start to die and they think that the killer is one of the ten.