Method for decoding received symbols by a receiver using a Lenstra-Lenstra-Lovász lattice reduction in a receiver receiving constellation points through a Multi Input Multi Output channel, from a matrix representing the Multi Input Multi Output channel which is decomposed into a unitary matrix Q, an upper triangular matrix R, and an unimodular matrix T, characterized in that the reduced upper triangular matrix R, the unitary matrix Q and the unimodular matrix T satisfy the following formula: M = QRT − 1, where M is an upper triangular matrix M of the Multi Input Multi where M is an upper triangular matrix M of the Multi Input Multi Output channel,the method is executed in a soft output decision algorithm and the size of the upper triangular matrix M is equal to the number of antennas N t minus one of a source which transmits the constellation points, contributions of assumed transmitted symbols are subtracted from the received constellation points and a prefiltering which takes into account the subtraction is performed in order to provide the upper triangular matrix M, the prefiltering W ẑ i F ẑ i being performed according to the following formula: F z ^ i = E i I + A − 1 e i † e i ρ ρ + | z ^ i | 2 | z ^ i | 2 + e i A − 1 e i † A − 1 H †, where e i is a row vector of size N t comprising all zeros entries but in the i -th position having a one, A = H † H +ρ -1 I, ẑ i is the i-th component of the transmitted vector of received symbols, H is a channel estimate between the source and the receiver, ρ is the signal to noise ratio, I is the identity matrix and E i is as an N t × N t identity matrix from which the i -th row is removed, W z ^ i † W z ^ i = A ' i E i A − 1 A − β e i † e i A − 1 E i † A ' i where β = ρ ρ + | z ^ i | 2 | z ^ i | 2 + e i A − 1 e i † + e i A − 1 E i † A ' i E i A − 1 e i † − 1., A ' i = E i A − 1 E i † − 1. the method comprises the steps of: - reducing the k-th column of the upper triangular matrix R and updating the unimodular matrix T into a new unimodular matrix, k being a variable indicating the rank of a column within the reduced upper triangular matrix R, - permuting the k-th and the k-1-th columns of the reduced upper triangular matrix R and of the new unimodular matrix T according to a comparison between the elements of the k-1th and k-th row of the k-th column of the reduced upper triangular matrix R, - triangularizing the reduced upper triangular matrix R of which columns are permuted into a new reduced upper triangular matrix and updating the unitary matrix Q into a new unitary matrix. - reducing the k-th column of the upper triangular matrix R and updating the unimodular matrix T into a new unimodular matrix, k being a variable indicating the rank of a column within the reduced upper triangular matrix R, - permuting the k-th and the k-1-th columns of the reduced upper triangular matrix R and of the new unimodular matrix T according to a comparison between the elements of the k-1th and k-th row of the k-th column of the reduced upper triangular matrix R, - triangularizing the reduced upper triangular matrix R of which columns are permuted into a new reduced upper triangular matrix and updating the unitary matrix Q into a new unitary matrix.