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This paper proposes a new detection algorithm for MIMO communication systems employing high-order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward application of the Belief Propagation (BP) algorithm yields very poor results. Our algorithm is based on an optimal tree approximation of the Gaussian density of the unconstrained linear system. The finite-set constraint is then applied to obtain a cycle-free discrete distribution. Simulation results show that even though the approximation is not directly applied to the exact discrete distribution, applying the BP algorithm to the cycle-free factor graph outperforms current methods in terms of both performance and complexity. The improved performance of the proposed algorithm is demonstrated on the problem of MIMO detection.