Having bought a model ship, the Unicorn, for a pound off a market stall, Tintin is puzzled that the sinister Mr. Sakharine should be so eager to buy it from him. When he refuses to sell it, Sakharine forces him and his dog Snowy to join his gang as they sail to Morocco on an old cargo ship.
Sakharine has bribed the crew to revolt against the ship's master, Captain Haddock, but Tintin, Snowy and Haddock escape, arriving in Morocco at the court of a sheikh, who also has a model of the ship. Haddock tells Tintin that his ancestor Sir Francis Haddock was forced to scuttle the original Unicorn when attacked by a pirate but managed to save his treasure and provide clues to its location in scrolls, hidden in models of the Unicorn.