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Cooperative transmission is an efficient technique to realize diversity gain in wireless fading channels via a distributed way. Cooperative automatic repeat request (ARQ) is known as a protocol which exploit spatial diversity by allowing the relay node to retransmit the source data packet to the destination node, when the latter is unable to decode the source node data correctly. In this short paper we derive closed form expressions for the spectral efficiency for C-ARQ scheme and we will also present a rate adaptive C-ARQ protocol. We consider a scenario in which both the source and relay nodes employ adaptive modulation. Our simulation results prove that the proposed scheme enhances the spectral efficiency noticeably when compared to other schemes.