In this paper, we present improvements in the estimation of frequency-dependent scaling function for non-uniform speaker normalization when compared to the method in . Further, unlike , using the estimated frequency-dependent scaling function, γ(f), we estimated the universal warping function that is necessary to separate out the speaker-dependent term as a translation factor and show that it is similar to mel-scale. Since, the proposed warping function is similar to mel-scale, we argue that our study "justifies" the usage of mel-scale in speech recognition, not only from the point of view of psychoacoustics but also from the view point of speaker normalization. Finally, in , we have assumed the commonly used formula for mel-scale, mel = 2595 log10 1 + f/700 for the universal warping function. In this paper, we have tried to fit a mel-like formula to the estimated universal warping function and use it to do non-uniform speaker normalization. We present the recognition results using these different universal warping functions with word error rate as the performance measure.