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Lattice reduction (LR) has recently emerged as a promising technique for improving the performance of suboptimal multiple-input-multiple-output (MIMO) detectors. For LR-aided MIMO detection, the Lenstra-Lenstra-Lovász (LLL) and Seysen's algorithm (SA) have been considered almost exclusively to date. In this paper, we introduced a new LR algorithm for LR-aided linear detection (LD). In contrast to the LLL and SA, which are targeted to search for bases with relatively short basis vectors, the proposed algorithm has been designed to improve the minimum Euclidean distance of the LR-aided linear detector, thus exhibiting improved error rate at high SNR. The error-rate performance of the proposed algorithm as well as the required complexity has been demonstrated through extensive computer simulations.