The μ-law proportionate normalized least mean square (MPNLMS) algorithm has been proposed recently to solve the slow convergence problem of the proportionate normalized least mean square (PNLMS) algorithm after its initial fast converging period. But for the color input, it may become slow in the case of the big eigenvalue spread of the input signal's autocorrelation matrix. In this paper, we use the wavelet transform to whiten the input signal. Due to the good time-frequency localization property of the wavelet transform, a sparse impulse response in the time domain is also sparse in the wavelet domain. By applying the MPNLMS technique in the wavelet domain, fast convergence for the color input is observed. Furthermore, we show that some nonsparse impulse responses may become sparse in the wavelet domain. This motivates the usage of the wavelet-based MPNLMS algorithm. Advantages of this approach are documented.