A block signal maximum likelihood detection (MLD) employing QR decomposition and M-algorithm (QRM-MLBD) can significantly improve the bit error rate (BER) performance of the single carrier (SC) transmissions in a frequency-selective fading channel, compared to the conventional frequency-domain equalization (FDE). In QRM-MLBD, the cyclic prefix (CP) is inserted in order to avoid inter-block interference (IBI). However, the CP insertion reduces the transmission efficiency. In this paper, we propose an overlap QRM-MLBD which requires no CP insertion. In overlap QRM-MLBD, IBI can be suppressed by overlapping consecutive observation windows and picking up only the reliable part after the block signal detection. We evaluate the average BER performance and the throughput performance by computer simulation to compare with the conventional QRM-MLBD with CP insertion.