This paper derives relationships between the moments of the scaling function psi₀(t) associated with multiplicity M, K-regular, compactly supported, orthonormal wavelet bases [6, 5] that are extensions of the multiplicity 2, K-regular orthonormal wavelet bases constructed by Daubechies. One such relationship is that the square of the first moment of the scaling function (psi₀(t)) is equal to its second moment. This relationship is used to show that uniform sample values of a function provides a third order approximation of its scaling function expansion coefficients. For the special case of M=2, the results in this paper have been reported earlier.