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The spectral subtraction method is historically one of the first algorithms proposed for noise reduction. However, most implementations and variations of the basic technique cannot suppress musical noise effectively, and keep residual noise and speech distortion under a low level simultaneously. In this paper, we analyze two foundational shortcomings of spectral-subtraction-like methods, and proposed a novel multi-band spectral subtraction based on phase modification and magnitude compensation. The new method outperforms the standard multi-band spectral subtraction method resulting in superior speech quality and greatly reduced musical noise.