The basis-motion torque composition (BMC), which generates feedforward torque for precise joint-trajectory tracking of a multi-joint robot arm, has been recently suggested. It is based on four arithmetical operations of time-series torque data of several motions preliminarily obtained by the iterative learning control. The remarkable advantage of BMC is to generate desired feedforward torque without prior information of dynamics parameters. However, the class of torque generated by the BMC has been restricted. The paper presents an enhanced BMC which permits generation of motions with different motion-velocity profiles among joints of a multi-joint robot. The algorithm is presented and the validity of algorithm is confirmed through numerical simulations in the case of a two-joint robot arm under the influence of gravity. Furthermore, a class of applicable systems of BMC approach is discussed.