A time-domain maximum likelihood block signal detection employing QR decomposition and M-algorithm (TD-QRM-MLBD) is a computationally efficient near ML detection scheme and 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 minimum mean square error based frequency-domain equalization (MMSE-FDE). In TD-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 iterative overlap TD-QRM-MLBD which requires no CP insertion. We evaluate the throughput performance of iterative overlap TD-QRM-MLBD by computer simulation to compare it with the conventional TD-QRM-MLBD with CP insertion.