A method of describing the nonlocality of the exchange and correlation energy and potential is used in a self-consistent spinless atomic calculation. The exchange and correlation potential V is analytically written and used in the calculation of the total energies and orbitals eigenvalues of the self-consistent Kohn-Sham equations for the atomic case. The results for the lighter atoms and for other examples are discussed and compared with the results obtained within the framework of the local-density approximation (LDA). We also present an analysis of the shape and asymptotic behavior of the potentials. A comparison of the outcome of the method with the results of LDA, Hartree-Fock calculations, and other approximate descriptions of nonlocality effects clearly indicates the power of the method.