In order to solve the problem of calibrating the position and orientation of an object on the robot hand with respect to the camera, Extended-eye-in-hand calibration is proposed from traditional eye-in-hand calibration, which extends the robot hand-eye relationship to extended hand-eye relationship. An assistant camera is introduced to accomplish robot extended-eye-in-hand calibration by using a planar calibration target and plenty of calibration points derived from the image feature of a rectangle on the robot extended hand. The results of the conducted real experiment illustrate the feasibility and validity of the method. The precision of the calibration depends on the precision of extended hand and the precision of the derived calibration points. In our experiment, the final Root Mean Square (RMS) is 0.113 mm.