Recently, a frequency-domain block signal detection (FDBD) using maximum likelihood detection (MLD) employing QR decomposition and M-algorithm (QRM-MLD) was proposed for the reception of the single-carrier (SC) signals transmitted over a frequency-selective fading channel. SC-FDBD with QRMMLD can significantly improve the bit error rate (BER) performance of SC transmission while reducing significantly the computational complexity compared to the MLD. However, its computational complexity is still high. In this paper, we propose a computationally efficient 2-step QRM-MLD SC-FDBD. Compared to conventional QRM-MLD, the number of symbol candidates can be reduced by using the decision made by minimum mean square error based frequency-domain equalization (MMSE-FDE). We evaluate the BER performance achievable by 2-step QRM-MLD and show that it can significantly reduce the computational complexity while keeping the BER performance almost the same as the conventional QRMMLD.