Given an industrial robot equipped with a dexterous hand and an object to be grasped with four grasping points determined on its faces, this paper deals with the problem of finding the joint configurations that allow to grasp that object. The proposed solution is based on an iterative optimization method that consecutively moves the joint that best contributes to reduce the distance of the fingertips to the desired locations. The method is particularized for a Stäubli RX90 robot and a dexterous hand MA-I with four fingers developed at the IOC’s Robotics Lab.