A small plane departs from Paris to London. One of the passengers, Jane Gray, is not indifferent to the young man sitting in front of her, Norman Gael, a dentist whom she had already met once.
During the flight, Lady Horbari calls her maid from another cabin. A bee flies in the cabin, and one of the passengers kills her.
Shortly before arrival, one of the passengers, Madame Giselle, is found to be dead. About three quarters of an hour ago, the steward brought her coffee. One passenger, Dr. Bryant, states that death occurred half an hour ago. On the plane is the famous detective Hercule Poirot. He sees a deceased injection mark on his neck. It is believed that a woman was bitten by a wasp, but Poirot finds a native dart near her with a yellow-black piece of cloth that is blown out of a special tube. Someone fired a dart, smearing it with poison. The stewards did not notice anything suspicious in the behavior of Madame Giselle. They know her, quite often flew this flight.
Police inspector interrogates passengers. Mr. Clancy, the author of detective novels, reports that he once bought a tube for shooting darts, but she lies at his place. The tube is found under the seat where Hercule Poirot was sitting.
On the inquiry, it turns out that the real name of the deceased was Madame Marie Morisot. She was one of the most business lenders in Paris. Killed by Madame Moriso was a rare snake venom. None of the passengers knew the deceased, and no one noticed anything. The investigation is at an impasse, but one of the jurors suspects Hercule Poirot.
After the inquiry, Norman becomes interested in Jane, and they decide to figure out what is happening.
Police collect information about Madame Moriso. She was a true professional in her field, a scrupulously honest woman. She had a daughter, Annie, who did not live with her and had not seen her for many years. After the death of her mother, the girl receives a large sum. Maid Madame Morisot, Eliza, was instructed by her mistress to burn all her papers if something happened to her, and now all the documents have been destroyed.
The police together with Poirot discuss which of the passengers could kill Madame Moriso, but no one could go up to her unnoticed. Poirot notes that the pipe was placed under the seat, not thrown away. He asked for a detailed list of belongings of passengers.
In Paris, Poirot visits Madame Morisot's office. Her maid, Eliza, speaks well of her mistress and tells that Madame Moriso had an illegitimate daughter, whom she never told anything about. Eliza gives Poirot the notebook that Madame Moriso was looking for before the trip and could not find. Eliza burned the papers, and left the book, since she had no indications on this score.
After examining the book and asking the doorman Madame Morisot, Poirot learns that Lady Horbari was at the deceased the day before.
Police find a shop selling darts and tubes, but the fabric on them is only red.
Poirot arrives at the airline, where Madame Morisot bought a ticket. Under his pressure, the employee admits that the unknown paid him a large sum to sell Madame Moriso a ticket for this particular flight, justifying that there were no tickets for another flight.
Lady Horbari's husband, Stephen, is worried that she borrowed money from Madame Moriso. He is clearly not indifferent to the girlfriend of his wife Venetia, in love with him.
Jane is interested in the young archaeologist Jean Dupont, who was flying with her on the same plane, but the girl is in love with Norman. Hercule Poirot meets them and asks Jane to help him in the investigation, playing the role of his secretary. Norman Poirot proposes to play the role of blackmailer Lady Horbari. At first, the dentist is horrified, but then agrees. In a conversation, Norman mentions a farm in South Africa that he visited.
Poirot talks to the stewards and finds out that there were two coffee spoons on Madame Morisot's table.
Under the guise of a blackmailer, a make-up Norman comes to Lady Horbari. He demands a large sum for silence that the lady spent several days with the famous actor. After his departure, the lady visits Hercule Poirot. The woman admits that she lost a large sum of cards, and her friend actor advised me to turn to Madame Moriso. The deceased demanded to return the debt, threatening to tell everything to her husband, but the lady was not involved in her death. Poirot advises Lady Horbari to give her husband a divorce and agrees to accept child support from him.
Poirot asks Jane to go with him to Paris, find Jean Dupont and talk with him about the expedition.
To the lawyer, Madame Morisot comes her daughter, showing her inheritance rights. She is married to Mr. Richards, who lives in America. Poirot meets Madame Richards. She worked as a manicurist, then a maid, but a month ago she met Mr. Richards and is now about to leave for him. Poirot has no doubt that in front of him is the daughter of Madame Morisot, but it seems to him that he has already seen her somewhere. The detective recalls that he saw her on the plane - this is the maid of Lady Horbari.
Poirot wants to find Annie, but finds out that she is dead. She was found in a train with a prussic acid bubble in her hand.
Leaving Jane in Paris, Poirot returns to London. Soon Jane arrives, and Poirot gathers everyone to announce that he uncovered the crime.
They put the tube under the chair so that it would be found and decided that a dart was fired from it. But to shoot a dart from the tube so that it would definitely hit the right place is almost impossible, so the famous detective concluded that the poison dart was thrust in with his hand. The killer went to Madame Moriso, stuck a poisoned dart in her neck, then threw it out and released the wasp so that everyone would decide that the passenger had died from an insect bite. After examining the list of contents of the pockets and baggage of passengers, Poirot saw that Norman had an empty matchbox in his pocket and a white jacket in his suitcase.
Wearing a white jacket, Norman went to Madame Moriso under the guise of a steward offering coffee, and killed her. Therefore, two spoons turned out to be on the murdered table.
Madame Morisot's death could be beneficial to her daughter and the only passenger who spoke with her was Lady Horbari. Suspecting the murder of Norman, Poirot asked him to play the role of a blackmailer and made sure that he was an excellent actor. The famous detective guessed that Norman came to the agency and asked to sell Madame Morisot the ticket for the flight he needed.
Fearing for Jane, Poirot took her to Paris. Upon inquiry, he found out that Norman's real name was Richards. He visited a farm in South Africa, which is actually a snake nursery. After meeting Annie and learning about the relationship between her mother and Lady Horbari, Norman arranged for them to fly on the same plane, and Lady Horbari was suspected of murder. But then Norman fell in love with Jane and decided to remove Annie.
Poirot sympathizes with Jane and foresees two weddings: Venetia with Lord Horbari and Jane with Jean Dupont.
