Given the topography of its location, the ground level for the foundations of the cloister was raised nearly five feet above the level of the floor plan of the cathedral, and in a way that it could in future support the weight of the two heights, which came to pass upon the investiture of Cardinal Cisneros.
Arhitekt Rodrigo Alfonso in stavbenik Alvar Martínez sta nadzorovala gradnjo štirih koridorjev s štiristranskimi oboki.