Wavelets with different integer scaling factor M can be combined in an orthonormal wavelet transform provided they share the same scaling function. These multi scale discrete wavelet transforms are not restricted to dyadic or M-scale signal sizes. Wavelets of this kind have recently been applied in meteorology to describe the background error covariance’s in the numerical weather prediction model ALADIN. In this note, we give mathematical details of the structure of these wavelets. We explicitly construct 2 multi scale wavelet families, based on M-scale generalizations of the Haar and Meyer wavelets.