MIMO systems exploit multi-path propagation to improve throughput and performance of digital communication systems. However, at the receiver side, the computation of Euclidean distances requires prohibitive computational complexity particularly when combined with a high-order constellation. Conventionally, it is necessary to calculate all the Euclidean distances to find the maximum likelihood solution. In this letter, we propose a novel approach based on the principle of conditioned detection combined with lattice-reduction techniques to estimate the closest point to the received symbol without the computation of all the Euclidean distances. Thanks to this approach, a reduction up to 95% of the required number of multiplications is achieved without any degradation in terms of performance by comparison with a conventional BP technique.