A Computerized systematic investigation is carried out in order to design an axially symmetric electrostatic lens operated under zero magnification mode with an acceptable first order properties and small relativistic spherical and chromatic aberrations. The study is based on the analysis of axtal potential distribution according to the principle of synthesis. For specific axial potential distribution, the relativistic trajectory equation is solved in paraxial and non-paraxial approximation to provide the charged particle trajectory and its derivatives in both approximations. From these information s, the optical properties such as focal length , radius of spherical and chromatic aberration discs and the relativistic spherical and chromatic aberration coefficients are evaluated. General conclusion are drawn for the axial potential function that have small aberration coefficients for two types of electrostatic lenses . The electrode shapes and beam trajectory of an optimized potential with small aberration are also given .