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Directional antennas in ad hoc networks offer many benefits compared with classical omnidirectional antennas. The most important include significant increase of spatial reuse, coverage range and subsequently network capacity as a whole. On the other hand, the use of directional antennas requires new approach in the design of a MAC protocol to fully exploit these benefits. Unfortunately, directional transmissions increase the hidden terminal problem, the problem of deafness and the problem of determination of neighbors' location. In this paper we propose a new MAC protocol that deals effectively with these problems while it exploits in an efficient way the advantages of the directional antennas. We evaluate our work through simulation study. Numerical results show that our protocol offers significant improvement compared to the performance of omni transmissions.