Encouraged by the accounts of the new discoveries which had been made in the last expedition, Velasquez fitted out a new armament of four ships; two of which had been on the former voyage, and the other two he now purchased.  This expedition was to be commanded in chief by his relation Juan de Grijalva, under whom Pedro de Alvarado, Francisco de Montejo, and Alonso de Avila were captains, all persons of known bravery, and proprietors of estates in these islands.  For this equipment, each captain provided sailors and provisions, and the governor furnished ships, arms, and other necessaries.  The accounts which had been circulated of the riches of the country, especially from the information of Melchior the native, soon collected a number of unprovided adventurers from the different islands, so that 240 companions speedily engaged for the expedition, among whom I resolved to try my fortune once more.  We each deposited a certain stipulated sum, to provide various necessary articles for the voyage, and for our use when in the field.  The orders given on the occasion by Velasquez to Grijalva were, to bring back as much gold and silver as he could procure, and in regard to colonization or settlements, he left him to act according to circumstances as he might think best.  We had the same pilots as on the former voyage, with a fourth, whose name I do not remember; Penalosa was our veedor, and Juan Diaz our chaplain.  The port of Matanzas was chosen as the most convenient rendezvous, as the colonists had many plantations and flocks of swine in that neighbourhood.

All our preparations being made, we set sail on the 5th of April 1518, after hearing mass with great devotion, and in ten days doubled the point of Guaniguanico, which the pilots call Cape St Antonio.  In eight days more we came in sight of the island of Cozumel, the currents forcing us farther down than we had been in our former voyage.  On sight of our ships, the natives fled from a town on the island, but our people found two old men concealed in a field of maize who were unable to follow the rest.  Our interpreters, Julianillo and Melchiorejo, whom we had made prisoners in the former voyage, understood the language of these people, as the island of Cozumel is only four leagues from their country.  Grijalva treated these people well, after which he gave them some presents and dismissed them, being in hopes to induce the natives of the town to return.  Some time afterwards, an Indian woman of a good person and handsome countenance joined us, who spoke the language of Jamaica, which is the same with that spoken in Cuba.  She told us that she had left Jamaica two years before in a canoe, with her husband and nine other men, intending to fish at certain islands; but the currents had driven them to this place, where the natives sacrificed her husband and all her other companions.  Expecting that this woman might prevail on the natives to return to the town, Grijalva sent her away for that purpose, allowing