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In this paper, theoretical electro-optical characteristics of a modified cylindrical mirror analyzer based on three coaxial cylindrical electrodes obtained with numerical calculations are presented. It was shown, for the first time, that the image of a point source of electrons located on the analyzer optical axis is in the form of a circle which does not depend on the entrance angle of electrons into the analyzer within the range of angles α = 30°– 40°. In particular, for the input angle α = 36° and dispersion Δα = ±3°, the relative energy resolution is equal to 0.01% at the analyzer constant K = 1.97.