This paper proposes a new method to construct wavelets decomposing and reconstructing matrices of wavelet coefficients without iterative calculation in symmetrical extension for finite length signal, and correspondingly gives the base vectors and basis images of 9/7 wavelet. The matrices can be used for image partition processing based on wavelet method. As an example,the application of wavelet transform matrices constructed in this paper in FRIT image denoising will not only reduce the calculation greatly but also improve on the edge effect evidently compared with the periodic prolongation method.