The paper proposes a new approach to the problem of determining optimal form-closure grasps of polygonal objects using four frictionless contacts. A new set of grasp parameters is determined based only on the directions of the applied forces. These parameters are used to obtain a new formulation of the necessary and sufficient condition for the existence of four-finger frictionless form-closure grasps, as well as to determine the optimal grasp. Given a set of contact edges, using an analytical procedure a solution that is either the optimal one or is very close to it is obtained (only in this second case an iterative procedure is needed to fins a root of a non-linear equation). This procedure is the used for an efficient determination of the optimal grasp on the whole object. The algorithms have been implemented and numerical examples are shown