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A relaying technique based on single-relay selection is studied for multiple-relay networks when hierarchical modulation is employed for unequal error protection. A single-relay selection scheme achieves a higher bandwidth efficiency while maintaining the same diversity order as when all the relays are selected in a multiple-relay network. Specifically, a cooperative network with one source, K relays, and one destination is considered in which two different protection information classes are modulated by a hierarchical 2/4-amplitude shift keying (ASK) constellation at the source. After selecting a relay to cooperate with the source, based on the instantaneous received signal-to-noise ratio, the selected relay decides to retransmit both classes by using a hierarchical 2/4-ASK constellation, or the more protection class by using a 2-ASK constellation, or remains silent. The approximated bit error rate (BER) of each information class is derived. Optimal thresholds are chosen to minimise the BER of one class while the BER of the other class satisfies a requirement. Numerical and simulation results are provided to validate the analysis. The results also show that the optimal thresholds can improve the error performance significantly.