The classic Shilov-Dukhin theory of the low frequency dielectric dispersion of colloidal suspensions in binary electrolyte solutions [Shilov, V. N.; Dukhin, S. S., Colloid J. 1970, 32, 245.; Dukhin, S. S.; Shilov, V. N. Dielectric Phenomena and the Double Layer in Disperse Systems and Polyelectrolyies; Wiley: New York, 1974] was developed for the frequency range corresponding to the concentration polarization phenomenon: up to a few megahertz. While a few extensions to a broad frequency range including the Maxwell-Wagner-OKonski dispersion exist, they all consist of modifications of the final results of the theory rather than modifications of its hypothesis, extending their validity to high frequencies. In this work we avoid this artificial process by providing a high frequency extension fully from within the theory.