We derive a fast maximum likelihood based (MLB) decoder for a multi-input multi-output (MIMO) Rician fading channel with additive white Gaussian noise (AWGN). The basic idea is to take profit of the Rician channel structure to significantly reduce the search of the optimum vector of symbols by the ML criterion. When channel diversity is low, we obtain bit error rates (BER) which are very close to the BER of the maximum likelihood (ML) optimum decoder. Comparisons in terms of BER for Quadrature Amplitude Modulation (QAM) are performed for the MLB, ML and OSIC (Ordered Successive Interference Cancellation) decoders via simulations. Finally, the ratio of computational complexities (depending of the number of transmitters and on the constellation), between the ML and the MLB is presented to show the interest of the proposed approach.