Near maximum likelihood block signal detection using QR decomposition and M-algorithm (QRM-MLBD) can improve a bit error rate (BER) performance of cyclic prefix inserted single-carrier (CP-SC) transmissions. However, it requires a fairly large number M of surviving paths in the M-algorithm and leads to very high computational complexity. Replacing the CP by training sequence (TS) was shown to reduce the number of M. Another approach to reduce the complexity of QRM-MLBD is to modify the tree structure constructed by QR decomposition for ML detection. Recently, we proposed a 2-step QRM-MLBD which prunes unreliable symbol candidates before tree search by using the minimum mean square error based frequency-domain equalization (MMSE-FDE) output. In this paper, we apply the 2-step QRM-MLBD to TS inserted SC (TS-SC) transmission in order to further reduce the complexity of QRM-MLBD. We show by computer simulation that 2-step QRM-MLBD can reduce the complexity compared to conventional QRM-MLBD while keeping almost the same BER performance.