The present invention aims to provide a method for fast and exact ML low-complexity demodulation in for example MIMO systems. The present invention relates to a method and arrangement for processing signals, especially a Maximum Likelihood (ML) demodulation of Quadrature Amplitude Modulation (QAM) signals, in a digital communications system, having a number of transmit antennas transmitting nT symbols, the method comprises the steps of: using xm, denoting symbols transmitted, wherein m=1 . . . nT, given a channel, selecting i and j and making pre-calculations facilitating finding a best combination of Xl . . . Xi−1, Xi+1 . . . Xj−1, Xj+1 . . . XnT for any given Xi, Xj and a received signal, going through every combination X1 . . . Xi−1, Xi+1 . . . Xj−1, Xj+1 . . . XnT and projecting in a number of directions for each of said combinations and generating a list of candidate combinations of Xi and Xj for each combination X1 . . . Xi−1, Xi+1 . . . Xj−1, Xj+1 . . . XnT, and hence generating a list of candidate combinations X1 . . . XnT, and providing a maximum-likelihood symbol combination.