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In this letter, we introduce a novel technique to speed up the famous LLL lattice reduction algorithm by use of sorting. Simulation results reveal that when applied to LLL-reduction-aided MIMO detectors, our proposed joint sorting and reduction technique can find an LLL-reduced basis with the average number of basis vector swappings reduced by about 47.5% for a 2 times 2 system and more for higher dimensional systems, without degrading the detection performance. Moreover, when the maximum number of vector swapping is limited, our proposed algorithm significantly outperform the conventional one at low-to-moderate bit error rates. This suggests that it can be applied advantageously to those MIMO systems with a strict delay constraint.