Multifingered robot hands are necessary for robots in order to realize many tasks. Many researches on decision of contact points of multi fingered robot hands have been performed in order to minimize fingertip force for a given task. Some of these methods, however, take much time until decision of fingertip position because nonlinear programming problem including friction condition is solved for all combinations of candidates of fingertip positions. This paper proposes a new algorithm using the optimization indexes of fingertip force derived from norm of manipulating force and angle limits of grasping force vector derived from condition of static equilibrium. By using the indexes, unnecessary candidates are deleted in advance to realize fast decision of fingertip position. Lastly, numerical verification for the proposed method is performed.