A small plane departs from Paris to London. One of the passengers, Jane Gray, is not indifferent to the young man Norman Gael, the dentist with whom she met once, is sitting in front of her.
During the flight, Lady Horbury summons her maid from another salon. In the cabin a bee flies, and one of the passengers kills her.
Shortly before the arrival, it appears that one of the passengers, Madame Giselle, is dead. About three-quarters of an hour ago the steward brought her coffee. One of the passengers, Dr. Bryant, establishes that death came about half an hour ago. The plane is the famous detective Hercule Poirot. He notices on his neck the deceased trail of the injection. It is believed that a woman was bitten by a wasp, but Poirot finds near her a native dart with a yellow-black piece of cloth that is blown out of a special tube. Somebody released such a dart, smeared it with poison. Stewards did not notice anything suspicious of the behavior of Madame Giselle. She is familiar
to them, quite often flew this flight.
The police inspector interrogates the passengers. Mr. Clancy, the author of detective novels, reports that he once bought a tube for shooting darts, but she is lying at his house. The pipe is found under the seat where Hercule Poirot was sitting.
At the inquest it turns out that the real name of the deceased was Madame Marie Morisot. She was one of the most business moneylenders 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 comes to a standstill, but one of the jury suspects Hercule Poirot.
After the inquiry, Norman is interested in Jane, and they decide to figure out what is going on.
The police collect information about Madame Morisot. She was a true professional, scrupulously honest woman. She had a daughter, Annie, who did not live with her and for many years did not see her. After the death of the mother, the girl receives a large sum. Madame Moriso’s maid, Eliza, received instructions from her landlady to burn all her papers if something
happened to her, and now all the documents have been destroyed.
The police, together with Poirot, discuss who of the passengers could have killed Madame Morisot, but no one could go unnoticed by her. Poirot draws attention to the fact that the tube was placed under the seat, and not thrown out. He asks for a detailed list of the things of the passengers.
In Paris, Poirot visits the office of Madame Morisot. Her maid, Eliza, speaks well of her mistress and tells that Madame Morisot had an illegitimate daughter, whom she never told anything about. Eliza gives Poirot a notebook, which Madame Moriso was looking for before the trip and could not find. Eliza burned the papers, and left the book, since she had no instructions on this score.
After studying the book and asking the doorman Madame Morisot, Poirot discovers that Lady Horbury was at the deceased’s eve.
The police find a shop in which darts and pipes are sold, but the fabric on them is only red.
Poirot comes to the airline, where Madame Morisot bought a ticket. Under his pressure, the employee admits: an unknown person paid him a large sum to sell the ticket to Madame Moriso on this flight, justifying that there is no other ticket for another flight.
The husband of Lady Horbury, Stephen, is concerned that she borrowed money from Madame Morisot. He is clearly not indifferent to the friend of his wife Venetia, in love with him.
Jane is interested in a young archaeologist Jean Dupont, flying with her in the same plane, but the girl is in love with Norman. They meet Hercule Poirot 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 Horbury. First the dentist is horrified, but then agrees. In conversation, Norman mentions a farm in South Africa, which he visited.
Poirot talks to the stewards and finds out that there were two coffee spoons on the table of Madame Morisot.
Under the guise of a blackmailer, Norman comes to Lady Horbury. He demands a large sum for the silence that the lady spent several days with the famous actor. After his departure, the lady visits Hercule Poirot. The woman admits she lost a large amount of money in the cards, and her friend advised him to turn to Madame Morisot. The deceased demanded to return the debt, threatening to tell her everything to her husband, but the lady was not involved in her death. Poirot advises Lady Horbury to give her husband a divorce and agrees to take alimony from him.
Poirot asks Jane to go with him to Paris, find Jean Dupont and talk to him about the expedition.
To the lawyer Madame Moriso comes her daughter, claiming her inheritance rights. She is married to Mr. Richards, who lives in America. Poirot meets with Madame Richards. She worked as a manicurist, then as a maid, but met Mr. Richards a month ago and is about to leave for him. Poirot does not doubt that before him is the daughter of Madame Morisot, but it seems to him that he has already seen her somewhere. The detective remembers that he saw her on the plane – this is the maid of honor Horbury.
Poirot wants to find Annie, but finds out that she is dead. She was found on the train with a bubble of hydrocyanic acid in her hand.
Leaving Jane in Paris, Poirot returns to London. Jane soon arrives, and Poirot collects everyone to announce that he has uncovered the crime.
The tube was put under the armchair so that it was found and decided that a dart had been fired from it. But to shoot from the tube with a dart so that it definitely fell into the right place is almost impossible, so the famous detective came to the conclusion that a poisonous dart was pierced. The murderer approached Madame Morisot, thrust a poisoned dart into her neck, then threw it away and released the wasp so that everyone decided that the passenger had died from an insect bite. After examining the contents of the passengers’ pockets and luggage, Poirot saw that Norman had an empty matchbox in his pocket, and in his suitcase a white jacket.
Wearing a white jacket, Norman went to Madame Morisot in the guise of a steward offering coffee, and killed her. Therefore, two spoons were found on the table.
The death of Madame Morisot could be beneficial to her daughter and the only passenger who spoke to her – Lady Horbury. Suspecting the murder of Norman, Poirot asked him to play the role of blackmailer and made sure that he is an excellent actor. The famous detective guessed that Norman had come to the agency and asked to sell Madame Moriso a ticket for the flight he needed.
Fearing for Jane, Poirot took her to Paris. Making inquiries, he learned that the real name of Norman was Richards. He was on a farm in South Africa, which in fact is a snake nursery. After getting acquainted with Annie and learning about the relationship between her mother and Lady Horbury, Norman arranged so that they flew by one plane, and the suspicion of murder fell on Lady Horbury. But then Norman fell in love with Jane and decided to remove Annie.
Poirot sympathizes with Jane and foresees two weddings: Venetia with Lord Horbury and Jane with Jean Dupont.