A method and apparatus for Multiple-Input Multiple-Output (MIMO) signal decoding using complex Lattice Reduction (LR) in a multiple antenna system is provided. The method provides MIMO signal decoding with increased operating speed using a transformation of reducing the lattice basis directly to a complex channel matrix that has a smaller size in comparison with a conventional matrix, which decreases the computational complexity of the LR transformation, as well as using a procedure of permutating columns of the channel matrix only twice without binding to the procedure of reducing off-diagonal elements of the matrix R, namely prior and after the procedure of reducing. Moreover, the new method for MIMO signal decoding has its output soft decisions.