Snowy gets into a fight with a neighbor's cat and the ship breaks. A scroll comes out of the mast of the ship. Tintin later finds the scroll and puts it in his wallet. Silk who is a well known thief, steals the wallet containing the scroll. Tintin visits Sakharine who tells him about two other model ships.
Not long after, Tintin is abducted by Sakharine's men. They lock him up in a ship. Tintin manages to escape and goes to meet the captain of the ship known as Haddock. Haddock at the time is drunk as a result of consuming so much wine given to him by one of Sakharine's men known as Allan. Tintin decides to run away with Snowy taking Haddock with him.
Sakharine sends a seaplane after them. Tintin captures the plane and they use it to fly. The plane crashes in the desert. While there, Haddock starts to hallucinate. He recalls a story about one of his forefathers Francis Haddock whose ship loaded with treasure was attacked by pirates. Francis decided to sink the ship than allow the pirates het hold of its treasure. He recalls the existence of three models of the ship each containing a scroll. The three scrolls put together will reveal the location of the sunken Unicorn.
At the end, Tintin retrieves all three scrolls. Tintin and Haddock locate some of the treasure and continue the search for the entire ship.