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, especially when the source-relay channel state information (CSI) is not available at the destination. In this study, the authors investigate the SNR-based selection relaying scheme in a multi-relay cooperative network (with R potential relay nodes) and examine the impact of the error propagation on the end-to-end performance of the system. The authors derive closed-form expressions for the end-to-end symbol error probability (SEP) of the system for both identically distributed and non-identically distributed Rayleigh fading environments. In the analysis, the authors consider M-ary phase shift keying (M-PSK), M-ary pulse amplitude modulation (M-PAM) and M-ary quadrature amplitude modulation (M-QAM) schemes. They also propose a class of geometry-independent thresholds that effectively mitigate the error propagation and provide full diversity of order R+1. Furthermore, for the special case of single-relay network, the authors derive closed-form expressions for the optimal thresholds that minimise the end-to-end SEPs.