Experimental evidence is presented showing that for magnetic multilayers measured in the CPP mode (current perpendicular to the planes), the magnetic-field dependence of the magnetoresistance MR(H) is dominated by scattering processes in which the electron is scattered by the potential due to pairs of neighboring magnetic layers. It is demonstrated experimentally that curtailing such scattering processes leads to a significant decrease in MR(H). These results are confirmed by a calculation.