Abstract: A new fast algorithm for the reconstruction of two-dimensional image from projection is described. The algorithm is based on the Chebyshev-Fourier decomposition of Hakopian polynomial.In contrast to our 2004’s work,the new algorithm retains its merits,while the computing time is improved remarkably. Moreover,compared with the traditional FBP method,the new algorithm can be applied for local image reconstruction.Computer simulation experiments show that the new algorithm is effective.