This research focuses on robot hand control of telexistence robot to realize precise hand manipulation. A humanoid surrogate robot which possesses large number of DoF and works under master-slave controlling can reproduce operator's hand and finger movements, and therefore it will realize fine and delicate teleoperation as if the work were performed by operator's own hand. However, even though the robot hand moves with dexterity, the body size difference between operator and robot has great influence to the consistency of position and configuration of body-parts such as fingertips between them, and may lead the difficultly of manual teleoperation. The problem is how to manage various operator's body size and maintain the correspondence of the operator to the robot. To overcome this issue, we propose a novel method of robot hand control which is based on congruence of two vectors bellows: (1) thumb tip to opposite fingers and (2) point-of-view to thumb/fingers. Considering that the spatial relationship between thumb and opposite fingers are important to perform precise hand manipulation, to keep the vector makes replication of operator's handshape on the robot hand. Also, because the operator of telexistence robot sees robot's body-parts including hand via eye-camera as his/her surrogate body, to match the vector realizes consistent experiences about hand position and aids intuitive operation. The proposed method was implemented to the control system of newly developed telexistence robot 'TELESAR6' and the performance of hand manipulation using the method was evaluated.