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This letter proposes a new MIMO precoding method for dual-stream data transmission based on the criterion of minimum Euclidean distance. The problem is optimally solved by expanding an ellipse within a 2-dimensional lattice to the maximum extent. A closed-form expression of minimum Euclidean distance is derived for square quadrature amplitude modulation (QAM) constellations. The ellipse expanding method (EEM) allows for very efficient implementation by checking a small lookup table with respect to the condition number of channel matrix. Illustrative examples validate the promising performance of the proposed method in comparison with existing schemes.