A method of maximum likelihood decoding for detecting the signals transmitted over a Multiple-Input-Multiple-Output (MIMO) channel of a communication system in which there are N co-channel transmit antennas and M co-channel receive antennas. In a first method an orthotope (22) is generated in input signal space centred on an approximate transmit signal point .tau. which is an inverse mapping from an actual received signal point (y) in output signal space. Only possible transmit points located within the orthotope are considered as candidate points and are transformed into corresponding candidate receive signal points in output signal space. The Euclidean distance between the candidate receive signal points and the actual signal point is calculated and the closest candidate receive signal is selected as the detected received point. In an alternative method, the orthotope is constructed as the smallest such orthotope which can contain a hyperellipsoid (20) in input signal space, which hyperellipsoid is a transformation from output signal space of a hypersphere (18) centred on the actual received signal point (y). Those transmit signal points which lie within the orthotope (22) but outside of the ellipsoid (20) are discarded and the remaining points within the orthotope are considered as candidate points, in the same way as described above.