A new method for initial design, the third-order aberration correction by using an iterative process, is presented to overcome the problems of the conventional method using third-order aberration theory. The aberrations of each lens group in the optical system are calculated individually and, iteratively under the constraint that aberrations of one group compensate for those of the other. groups. We applied the method to the design of a Petzval lens with an external entrance pupil. The result shows the capability of the method to provide an initial design for a complex optical system.