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Relay selection is crucial in improving the performance of wireless cooperative networks. Most of previous works for relay selection use the current observed channel conditions to make the relay selection decision for the subsequent frame. However, this assumption is often not realistic given the time-varying nature of some mobile environments. In this paper, we consider finite state Markov channels in the relay selection problem. Moreover, we also incorporate adaptive modulation and coding, as well as residual relay energy in the relay selection process. The objectives of the proposed scheme are not only to increase spectral efficiency, mitigate error propagation, but also to maximize the network lifetime. Simulation results are presented to show the effectiveness of the proposed scheme.