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The optimal "soft" symbol detection for spatial multiplexing multiple input multiple output (MIMO) system with known channel information requires knowledge of the marginal posterior symbol probabilities for each antenna. The calculation of these quantities requires the evaluation of the likelihood function of the system for all possible symbol combinations, which is prohibitive for large systems. It is however most often the case that most of the transmitted symbol combinations contribute only very little to these marginal posterior probabilities. We propose in this paper a suboptimal procedure which identifies the most significant symbol combinations via a sequential algorithm with Gaussian Approximation (SGA). Simulation results show that our method can approach the optimal a posteriori probability detector (APP) performance while being less complex than comparable suboptimal algorithms, such as the sphere decoder (SD). We further demonstrate that as opposed to the SD the complexity and memory requirements of our algorithm are fixed, therefore easing practical implementation.