Abstract: Robot dynamic model is usually written as H(q)q+C(q,q)q+G(q)=τ, where the matrix C can be properly defined so that H-2C is skew-symmetric. This property greatly facilitates robot controller design. It is believed that such C is uniquely determined. In this paper a new expression for robot the model is derived with the spatial notation developed in recent years, which shows that the matrix C with above property is not uniquely defined. Furthermore, the well-known robot adaptive control strategy proposed by Slotine and Li is taken as an example to demonstrate that replaced the traditional model with the new model presented in this paper, a much more computationally efficient adaptive control algorithm than the existing one can be obtained.