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Directional and smart antenna is an effective measure to improve the capacity of wireless ad hoc and sensor networks (WASN). To utilize the profit of directional and smart antenna, the MAC layer protocol has to be changed to adapt to the control of contention of the channel. A directional MAC (DMAC) protocol has been put forward before, but that protocol has some limitation which confines the MAC layer performance of WASN. To solve the problems of DMAC, a modified directional MAC (M-DMAC) protocol is designed in this paper, simulation results show that it improves the performance of DMAC.