Lattice reduction (LR) aided multiple-input-multiple-out (MIMO) linear detection can achieve the maximum receive diversity of the maximum likelihood detection (MLD). By emloying the most commonly used Lenstra, Lenstra, and L. Lovasz (LLL) algorithm, an equivalent channel matrix which is shorter and nearly orthogonal is obtained. And thus the noise enhancement is greatly reduced by employing the LR-aided detection. One problem is that the LLL algorithm can not guarantee to find the optimal basis. The optimal lattice basis can be found by the Korkin and Zolotarev (KZ) reduction. However, the KZ reduction is infeasible in practice due to its high complexity. In this paper, a simple algorithm is proposed based on the complex LLL (CLLL) algorithm to approach the optimal performance while maintaining a reasonable complexity.