In this paper, a new recursive implementation of composite adaptive control for robot manipulators is proposed. We investigate the recursive composite adaptive algorithm and prove the stability directly based on the Newton-Euler equations in matrix form, which, to our knowledge, is the first result on this point in the literature. The proposed algorithm has an amount of computation O(n), which is less than any existing similar algorithms and can satisfy the computation need of the complicated multidegree manipulators. The manipulator of the Chinese Space Station is employed as a simulation example, and the results verify the effectiveness of this proposed recursive algorithm.