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The use of directional antennas in ad-hoc networks has advantages such as high spatial reuse and extended antenna range. However it suffers from the deafness problem, which may significantly degrade the network performance. Recently, several directional MAC protocols have been proposed to manage directional antennas effectively and improve the network performance. However, the existing schemes do not adequately address the issues, because they do not consider the multi-rate environment and the overhead to establish communication with the adjacent devices. This paper presents a directional cooperative MAC scheme, in which data is delivered to a destination via a relay node equipped with a directional antenna. Simulation results show that the network performance is improved by using the proposed scheme.