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2-step maximum likelihood block signal detection employing QR decomposition and M-algorithm (QRM-MLBD) can significantly improve the bit error rate (BER) performance of single-carrier (SC) transmission while reducing the computational complexity compared to maximum likelihood detection (MLD). In 2-step QRM-MLBD, unreliable symbol candidates are removed by performing minimum mean square error based frequency-domain equalization (MMSE-FDE) prior to QRM-MLBD. However, a large number M of surviving paths is still required in the M-algorithm to achieve a BER performance close to the matched filter (MF) bound. In this paper, to remedy this problem, we introduce a detection ordering to 2-step QRM-MLBD. We will show by computer simulation that the use of detection ordering can achieve the same BER performance as 2-step QRM-MLBD while reducing the computational complexity.