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This paper proposes a two stage algorithm to improve the soft output of the channel demodulation algorithm for a multiple input multiple output (MIMO) system with block fading channels by the Monte Carlo method. In the first stage, the demodulation algorithm, i.e., probability data association detector (PDA) or minimum mean square error (MMSE) algorithm, computes the marginal probability distribution of symbols for each antenna. Then we draw samples from those marginal distributions and use the importance sampling algorithm to correct those distributions to approximate the joint posterior distribution of symbols for all the antennas. Simulation results are given to demonstrate the effectiveness of the new algorithm.