A new relative motion control methodology for a following system to an independent leading system is proposed for controlling relative position, velocity, and tension etc. It is based on maintaining minimum relative error between two independent systems. The control command of the following system to a leading system is generated by adding the current command and the output of the relative error compensation. The proposed control method is implemented on the experimental equipment which is a wire winding-unwinding system to control the tension of the line. The results show the unwinding system(follower) following the independent motion of the winding system(leader) to control the constant tension of the line in order to keep the roller dancer in reference position. The relative motion control method proposed in this paper can be applied to high precision equipment for unwinding and winding fine wire, fine fiber, and tape etc.