It is found that the nonlocality, introduced in the Woods-Saxon potential through an energy-independent effective mass approximation under the condition to keep unchanged the levels around the nuclear surface, gives rise, at m*g 0.9 m, to a 5 % increase in the RMS radii of nuclei from the mass zones A=155, 165, 173, 181, leading to a better agreement with the experiment. Thus, the nonlocality induces an increase in the mean-square radius leaving the mean kinetic energy almost unaffected.