Because hand is often used for grasping, developing a design of prosthetic hands, particularly light and compact underactuated anthropomorphic transradial prostheses for reproducing human hand complex grasping is crucial for upper-limb amputees. Obviously, the less the number of actuators is, the worse the anthropomorphic motion capability of the prosthetic hands will be. This paper aims to design a transmission mechanism with few motors actuating fingers which could serve the relatively accurate grasp movement of a human hand and has the potential to be embedded in a palm including the motors. We start with establishing an index for evaluating the anthropomorphic motion capability of a prosthetic hand. Based on the optimization of this index, we determine the number of actuators in fingers and the transmission relationship between the actuators and the metacarpophalangeal(MCP) joints. Then, a new design method to mechanically implement the transmission relationship based on a novel decomposition of transmission matrix is proposed in this paper. Utilizing this method, we obtained the final mechanical structure of a new prosthetic hand.