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QR decomposition and M-algorithm based near maximum likelihood block detection (QRM-MLBD) significantly improves the single-carrier (SC) multiple-input multiple-output (SC-MIMO) transmission performance in a frequency-selective fading channel. In the conventional QRM-MLBD, the cyclic prefix (CP) is inserted in order to avoid the inter-block interference (IBI). However, CP insertion reduces the transmission efficiency. In this paper, an iterative overlap QRM-MLBD is proposed for SC-MIMO transmission with no CP insertion. It is confirmed by computer simulation that the iterative overlap QRM-MLBD with no CP insertion provides improved throughput performance while reducing the computational complexity over the conventional QRM-MLBD with CP insertion.