Virtual reference is defined as the signal for a closed-loop System so that the response tracks the desired path perfectly. It is proposed to obtain a virtual reference signal suitable for a manipulator to track a predetermined trajectory using repetitive operations. Thus the algorithm ensures that the difference between the desired and the manipulator trajectories will become negligible as the number of operations approaches infinity if the manipulator is compensated for properly by local feedback. This algorithm uses a dual System to recursively improve the reference signal. Such a System has the advantage of being simple to design. The derivation of this algorithm is based on functional analysis. The effectiveness is confirmed by two experimental results.