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Cooperative diversity is a relatively new technique that can be used to improve the performance of the wireless networks. The main advantage of this technique is that the diversity gain can be achieved without the need to install multiple antennas at the transmitter or the receiver. In this paper, we investigate the performance of the best-relay selection scheme where the "best" relay only participates in the relaying. Therefore, two channels only are needed in this case (one for the direct link and the other one for the best indirect link) regardless of the number of relays (M). The best relay is selected as the relay node that can achieve the highest signal-to-noise ratio at the destination node. A general mathematical probability model is developed to study the outage performance of the best-relay selection adaptive decode-and-forward cooperative networks. In particular, closed-form expressions for the outage probability and average channel capacity are derived. Results show that the best-relay selection not only reduces the amount of required resources but also can maintain a full diversity order.