A new approach to XANES calculation is proposed and applied to Si and Fe K-edge XANES spectra to study the efficiency of this method. This method based on the partitioning technique includes important multiple scatterings in infinite order, but excludes unimportant multiple scatterings. The result of calculation for Si 35atom cluster shows that even if we include up to 7th multiple scatterings in the partial sum, the computation time is about 5% of that needed for the full multiple scattering calculation, and a good convergence to the full multiple scattering result is found. Similar result is obtained for iron clusters. The present study demonstrates the high efficiency and accuracy of this new method.