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Relay selection has been considered as an effective method to improve the performance of cooperative communication. However, the channel state information (CSI) used in relay selection can be outdated, yielding severe performance degradation of cooperative communication systems. In this study, the authors investigate how to select relays under outdated CSI in an amplify-and-forward cooperative communication system to improve its outage performance. The authors adopt maximum a posteriori (MAP) estimation to predict the actual signal-to-noise ratio (SNR) of each relay during data transmission and propose a single-relay selection (SRS) strategy based on the MAP estimation (SRS-MAP). To reduce the computational complexity, we approximate the a posteriori probability density of SNR and obtain a closed form of the predicted SNR. Simulation shows that SRS-MAP outperforms the relay selection strategies given in the literature. In order to further improve the outage performance, a new multiple-relay selection (MRS) method for outdated CSI is proposed, and by applying it to existing SRS strategies the corresponding MRS strategies are obtained. The authors find that the MRS strategies perform much better than their corresponding SRS ones and the MRS method improves the outage performance of cooperative communication system more effectively under outdated CSI than under non-outdated CSI.