Miss Marple and Mr Stringer are out soliciting donations for a charity. When they visit Mr Enderby, a rich and eccentric recluse, he appears at the top of the staircase and tumbles down, apparently the victim of a fatal heart attack. However, knowing that Enderby had a pathological fear of cats, Miss Marple becomes suspicious when she finds one in the house. When she goes to Inspector Craddock, he is skeptical.
Undeterred, Miss Marple eavesdrops when the family gather for the reading of the will. Each of the four heirs receives an equal share of the estate. His sister Cora declares that she believes he was murdered. The next day, when Miss Marple goes to see her, she finds Cora dead, murdered by a hatpin in the back. Cora's companion of many years, timid Miss Milchrest, can provide little information.
Miss Marple decides to take a "holiday" at the Gallop Hotel/riding school, as it is run by Cora's nephew Hector Enderby (Robert Morley) and the other two heirs are staying there. One of them, art expert George Crossfield, discovers the identity of the murderer, but is locked in a paddock with an excitable horse and perishes. An attempt is made to do away with Miss Marple herself, but is foiled by the intended victim (without her even realizing it).
By this point, Miss Marple knows the identity and motive of the killer, but has no definitive proof. She therefore lays a trap, pretending to have a heart attack at a dance at the hotel (while doing the Twist with Stringer). The police doctor has her placed in a room by herself, declaring it too dangerous to move her until morning. During the night, the criminal makes one last attempt to silence her, but Miss Marple is ready. The killer is revealed to be Miss Milchrest. She had been after Cora's seemingly worthless painting.