The disclosure relates to a method for decoding a received signal in a MIMO communication system and in at least one layer, each layer carrying at least one data symbol belonging to a signal constellation. The method includes, for one of the at least one layer, a maximum likelihood detection step. This step includes: selecting one candidate value for the data symbol of the layer, and determining the Euclidian distance between the received signal Y and the data signal transmitted using said candidate value multiplied by said channel matrix H, weighted by the inverse of a noise covariance matrix C such as ∥Y−ΣiHixi∥C−12, expressed as: Σi≠n∥Hi∥C−12|xi|2−2(HiHC−1Y−0.5Σj≠i,nHiHC−1Hjxj)x*i+∥Hn∥C−12|xn|2−2(HnHC−1Y−Σj≠nHnHC−1Hjxj)x*n=Σi≠nαiR(xi)2−2βiRxi+αnR(xn)2−2βnRxn+Σi≠nαiI(ℑxi)2−2βiIℑxi+αnI(ℑxn)2−2βnIℑxn. The terms depending on αk are computed by adding to each of them a predetermined constant depending on the size of the constellation of the layer k, called a constellation dependent constant.