Multilayers Fe (x)/ Pd (30 Angstrom) (6 Angstrom less than or equal to x less than or equal to 30 Angstrom) has been investigated by using transverse Kerr effect (TKE) method in a energy range from 1,3 to 3,6 eV. The oscillations of TKE with changing of the thickness of Fe layer has been observed. It was discovered that the value of period of oscillations is equal to 7 Angstrom. The off-diagonal element of permeability dielectric tensor epsilon (2)' has been calculated from measurements of TKE and optical constants for all multilayers. It has been found that the magnitude epsilon (2)'.omega (2) (where omega - frequency of incident light), proportional to the interband density of states oscillated with the same period of 7 Angstrom and the character of this oscillations was similar to the oscillations of Kerr effect. It should be emphasized that there were many distinctions between oscillations amplitudes of the saturation magnetization and TKE. The obtained results have been explained by the influence of finite-size effects on electronic structure of multilayers.