In this work, a new method is presented for generating the manipulator path which significantly reduces residual vibration under the torque constraints. The desired path is optimally designed so that the required movement can be achieved with minimum residual vibration. From the previous research works, the dynamic model had been established including both the link and the joint flexibilities. The performance index is selected to minimize the maximum amplitude of residual vibration. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link Manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path to both of unlimited and torque-limited cases.