Multiple-input multiple-output (MIMO) systems are playing an increasing and interesting role in the recent wireless communication. The complexity and the performance of the systems are driving the different studies and researches. Lattices Reduction techniques bring more resources to investigate the complexity and performances of such systems. In this paper, we look to modify a fixed complexity verity of the LLL algorithm to reduce the computation operations by reducing the number of iterations without important performance degradation. Our proposal shows that we can achieve a good performance results while avoiding extra iteration that does not bring much performance.