In this paper, we propose a spacial time slot scheduling algorithm for relay operation to improve the throughput performance of millimeter-wave wireless personal area network (mmWave WPAN) systems which employ directional antenna. The upcoming mmWave WPAN is designed for high definition TV (HDTV) transmission, high speed wireless docking and gaming, etc. Based on the fact that the significant path loss of millimeter-wave environments provides good space isolation, we have proposed a coexistence mechanism by sharing time slots for relay with direct transmission to guarantee throughput for the above data-rate-greedy applications. This paper is an extension that addresses spacial time slot scheduling for relay operation taking the effect of directional antenna into consideration. We model the throughput maximization with scheduling as an integer optimization and solve it by transforming the problem to a max-weight matching problem of a bipartite graph. We propose a scheduling algorithm based on the Kuhn-Munkres algorithm which can be used to solve the max weight matching problem. Simulation results show that there is up to 25% throughput improvement achieved compared with random scheduling method.