In multiple-input multiple-output (MIMO) systems, the use of lattice reduction methods, significantly improves the performance of suboptimal algorithms. Taking advantage of the temporal correlation of a Rayleigh fading wireless MIMO channel, a new method is proposed to reduce the complexity of lattice reduction methods by adaptively updating the reduced lattice basis. The proposed method achieves the same error performance as the original lattice reduction method, but significantly reduces the complexity of lattice reduction algorithms. The proposed method can be used with any lattice reduction algorithm and in any MIMO scenario that requires lattice reduction, such as MIMO detection, and broadcast cases.