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In distributed space-time (DST)-coded regenerative relay networks, demodulation error produced by relays degrades the receiver performance significantly. To mitigate this disadvantage, two threshold-based selective relaying schemes are proposed, that is, centralised selecting scheme and distributed selecting scheme, where each relay forwards signals only if its received signal-noise ratio is larger than a threshold. Both proposed schemes can work well with arbitrary modulation constellation and any number of relays and no matter whether the source-destination channel is available or not. Simulation results show both proposed selective relaying schemes outperform conventional schemes significantly and the improvement increases as the scale of relay network grows. Centralised selecting has a slightly better performance than the distributed selecting. However, the latter has a far lower system cost. This contribution provides two useful relaying mechanisms to mitigate error propagation.