Abstract: A kind of mother wavelet with good properties is constructed for any N≥2, which is differentiable for N times, converges to zero at the order O(|t|^-N) (t→∞) of and has N-2 order of vanishing movement and some property of symmetry meanwhile. A computation example for N= 4 is also given.

Key words: vanishing movement, scaling function, orthogonal mother wavelet