Although the power-spectral-subtraction (PSS) algorithm is widely used in speech enhancement, this method suffers from musical residual noise. So the enhanced speech sounds annoying to the human ear. This study proposes using the cross term between the spectrum of speech and noise signals to be additionally subtracted from the power spectrum of noisy speech, enabling background noise to be efficiently removed. Experimental results show that the proposed method can significantly improve the performance of the PSS algorithm by the consideration on the cross term. The quantity of musical residual noise can be efficiently removed, while speech components are well preserved in the enhanced speech.