The proposed algorithm is based on the exponential decay of the screened structure constants in the tight-binding (TB) Korringa–Kohn–Rostoker (KKR) Green function method and on a spatial truncation of the Green function in the spirit of Kohn's principle of nearsightedness of electronic matter. The KKR matrix equations are solved iteratively and non-zero electronic temperatures are used to accelerate the iterations. The dependence of the total energy accuracy on the size of the truncation region was investigated for large Cu and Pd supercells and it was found that total energy errors smaller than 2 meV could be achieved if the truncation region contained a few thousand atoms.