A new, very simple expression for the narrow aperture dimension of the horn is obtained and used in the optimum gain pyramidal horn design. The design parameters are computed from the simple and explicit formulas. These formulas do not need the application of the iterative methods, and are not restricted to the long-horn designs. The gain of a designed pyramidal horn is determined without approximating the path length error. Design examples are given to illustrate the performance of the design technique proposed in this paper.