Speech enhancement techniques using spectral subtraction have the drawback of generating residual noise with a musical character, so-called musical noise. We developed a new post-processing method for suppressing this musical residual noise. In this method, the auditory masking threshold is calculated twice, once before the spectral subtraction and once again afterwards. This ensures that all audible spectral signal components above the thresholds are detected. Audible components which are only present at the output are candidates for musical noise. Depending on their spectral bandwidth and time duration, they may be processed additionally. Using this post-processing, the distortion of the speech signal is not noticeable and musical noise is not audible even at low signal-to-noise ratios of about 0 dB.