Many parallel join algorithms have been proposed so far but most of which are developed focused on minimizing the disk It0 and CPU costs. The communication cost, however, is also an importantfactor that can significantly affect the join processing performance in multiprocessor system. In this paper we propose an eficient parallel join algorithm, called CubeRobust, for hypercube multicomputers. The proposed algorithm is developed based on the observation that the size ratio of two relations to be joined is the dominant factor in the communication cost. We develop the analytic cost model for the proposed join algorithm. The performance comparisons show that the Cube-Robustjoin algorithm works better than others proposed earlier in a wide range of size ratios.