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In order to avoid the resource inefficiency of all-participated cooperation in wireless amplify-and-forward relay networks, a novel relay selection scheme based on the channel gain of the source-relay and relay-destination links is proposed. A condition is introduced to maximize the upper bound of the overall received signal-to-noise ratio (SNR). The relay nodes which have bad channel conditions are excluded in turn from the cooperation so that their released resources can be reallocated to other nodes. This paper adopts a simplified power allocation scheme that assumes each selected relay has equal power. The total power is optimally assigned between the source and the relay set. Simulation results show that the proposed scheme can achieve similar BER performance with the scheme which employs all relays and optimal power allocation, but only applies a subset of available relays.