Abstract: A algorithm for construction the polynomial filter of compactly supported orthonormal wavelet by using Riesz lemma and the cosine triangular polymomial is proposed. A lot of compactly supported orthonormal wavelets are obtained by using this method. It is possible to choose "good" base from a lot of wavelets base. Especially,I.Daubechies's wavelets are constructed by applying this method. A few corresponding examples are also given.