Although, while he was in Cuba, he never found the Grand Khan, he never recalls the hopes which he has expressed.
He had discovered the island on its northern side by sailing southwest from the Lucayos or Bahamas.

From the eleventh of November until the sixth of December he was occupied in coasting along the northern shore, eventually returning eastward, when he crossed the channel which parts Cuba from Hayti.
The first course was east, a quarter southeast, and on the sixteenth, they entered Port-au-Prince, and took possession, raising a cross there.
At Port-au-Prince, to his surprise, he found on a point of rock two large logs, mortised into each other in the shape of a cross, so "that you would have said a carpenter could not have proportioned them better." On the nineteenth the course was north-northeast; on the twenty-first they took a course south, a quarter southwest, seeking in these changes the island of "Babeque," which the Indians had spoken of as rich with gold.

On the day last named Pinzon left the Admiral in the Pinta, and they did not meet again for more than a month.
Columbus touched at various points on Cuba and the neighboring islands.
He sought, without success, for pearls, and always pressed his inquiries for gold.

He was determined to find the island of Bohio, greatly to the terror of the poor Indians, whom he had on board: they said that its natives had but one eye, in the middle of their foreheads, and that they were well armed and ate their prisoners.
He landed in the bay of Moa, and then, keeping near the coast, sailed towards the Capo del Pico, now called Cape Vacz.

At Puerto Santo he was detained some days by bad weather.