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This work considers the application of Newton's iterative method of matrix inversion for reducing the complexity of calculating the unconstrained solution in Sphere Decoding (SD) for Multiple-Input Multiple-Output (MIMO) wireless communication systems. This paper also proposes a simpler initialization procedure for Newton's method. It is shown that as the size of the MIMO system increases, it becomes more tolerant to errors in the unconstrained solution for SD, and hence it requires a smaller number of Newton iterations. For a 16 × 16 MIMO system with QPSK or 16-QAM we show that 7 iterations are sufficient to ensure lossless SD performance. With only 4 iterations, a QPSK 32 × 32 MIMO system exhibits less than 0.1 dB performance loss relatively to SD employing the exact unconstrained solution.