The feature extraction process is a fundamental part of speech processing. Mel frequency cepstral coefficients (MFCCs) are the most commonly used feature types in the speech/speaker recognition literature. However, the MFCC framework may face numerical issues or dynamic range problems, which decreases their performance. A practical solution to these problems is adding a constant to filter-bank magnitudes before log compression, thus violating the scale-invariant property. In this work, a magnitude normalization and a multiplication constant are introduced to make the MFCCs scale-invariant and to avoid dynamic range expansion of nonspeech frames. Speaker verification experiments are conducted to show the effectiveness of the proposed scheme.