Discrimination between speech and music is important in many multimedia applications. In our previous work, focusing on the spectral change characteristics of speech and music, we presented a method using the mean of minimum cepstral distances (MMCD), and it showed a very high discrimination performance. In this paper, to further improve the performance, we propose to employ time-averaged MFCC in computing the MMCD. Our experimental results show that the proposed method enhances the discrimination between speech and music. Moreover, the proposed method overcomes the weakness of the conventional MMCD method whose performance is relatively sensitive to the choice of the frame interval to compute the MMCD.