The Moving Finger

The Moving Finger is technically a Miss Marple mystery, but Jane doesn't show up until the last third of the novel. The main character (and incompetent detective) is Jerry Burton, a pilot who's convalescing after a severe accident. He and his sister have taken a house in a village which is being plagued by poison pen letters. It's the usual Marple-style set-up, only without Aunt Jane. Until, that is, the local solicitor's wife dies suspiciously and suspicion falls upon, well, several people.  Mrs. Dane Calthrop, the vicar's wife, calls her friend Jane who visits, solves the mystery, and leaves with justice served and two couples paired off.  In other words, classic Christie.