A new LMS adaptive Volterra filtering scheme based on M-band discrete wavelet transformation (MDWT) is presented, where MDWT is employed along with power normalisation to decorrelate the Volterra input vector. In particular, the preprocessing procedure for the input vector decorrelation effectively reduces the eigenvalue spread of the input vector auto-correlation matrix, which improves the convergence rate of the adaptation process even in the case of wide classes of input signals.