Many parallel join algorithms have been proposed so far but most of which are developed focused on minimizing the disk I/O and CPU costs. The communication cost, however, is also an important factor that can significantly affect the join processing performance in multiprocessor systems. In this paper we propose an efficient parallel join algorithm, aclled Cube-Robust, 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-Robust join algorithm works better than others proposed earlier in a wide range of size ratios.