This paper presents a method for choosing a doublet design for the correction of longitudinal chromatic, spherical and coma aberrations. A secondary dispersion formula is utilized to sort out minimal longitudinal chromatic aberrations for the doublet. The program is developed with the Matlab software. An optimal doublet design to efficiently reduce both spherical aberration and coma will incorporate glass combination with a sufficiently large difference in the V-numbers and small powers. We succeed in obtaining an optimal doublet design with the proposed method.