Our paper is focused on a problem of analysis and design of a stigmatic optical system that has corrected third-order spherical aberration for an arbitrary position of the object. The relations for Seidel aberration coefficients of the system for an object at infinity that must be satisfied to ensure that the third-order spherical aberration does not depend on the position of the object are given. The method for obtaining design parameters of the initial optical system that can serve as a good starting point for further refinement using numerical optimization methods is proposed. Based on the use of modified formulas for third-order aberration coefficients, this method enables one to decide if the individual members of the optical system can be simple lenses or if these should be more complex elements (cemented doublets, triplets, etc.). As a final result, one obtains the design parameters of the above-mentioned optical system (radii of curvature, optical materials, axial separations between individual elements). The analysis is performed for a thin-lens representation of the system. The transition to the thick-lens optical system then can be done by mathematical methods of numerical optimization using commercially available optical design software. The proposed method is shown on a practical example of calculation of parameters of such an optical system.