In this paper, we propose a variant of the QRM-MLD signal detection method that is used for spatially multiplexed multiple antenna system. The original QRM-MLD signal detection method combines the QR decomposition with the M-algorithm, thereby significantly reduces the prohibitive hardware complexity of the ML signal detection method, still achieving a near ML performance. When the number of transmitter antennas and/or constellation size are increased to achieve higher bit rate, however, its increased complexity makes the hardware implementation challenging. In an effort to overcome this drawback of the original QRM-MLD, a number of variants were proposed. A most strong variant among them, in our opinion, is the ranking method, in which the constellation points are ranked and computation is performed for only highly ranked constellation points, thereby reducing the required complexity. However, the variant using the ranking method experiences a significant performance degradation, when compared with the original QRM-MLD. In this paper, we point out the reasons of the performance degradation, and we propose a novel variant that overcomes the drawbacks. We perform a set of computer simulations to show that the proposed method achieves a near performance of the original QRM-MLD, while its computational complexity is near to that of the QRM-MLD with ranking method.