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Error propagation from the relay to the destination is a major drawback of digital relaying protocols that substantially diminishes the cooperative diversity gain of the system. Appropriately designed selection relaying schemes can effectively mitigate this phenomenon and improve the diversity order, specifically when the source-relay channel state information (CSI) is not available at the destination. In this paper, we investigate the SNR-based selection relaying scheme and present a closed-form expression for the end-to-end symbol error probability (SEP) of the system for M-PSK modulation. The optimal threshold which minimizes the end-to-end SEP and provides full diversity order is also presented in closed-form. In our analysis, we examine the error propagation scenario in detail and derive a closed-form expression for the SEP under this scenario. Numerical results demonstrate that the SNR-based selection relaying scheme by employing the optimal threshold, without using error detection codes that reduce the bandwidth efficiency, effectively mitigates the error propagation and significantly improves the diversity order.