New expressions for the narrow aperture dimension of the pyramidal horn are presented. They are obtained by using a differential evolution algorithm (DEA), and are used in successfully designing optimum gain pyramidal horns. The DEA is a simple, fast, and robust evolutionary algorithm for solving general type of numeric optimization problems. Design parameters of the horn are determined from the simple and explicit analytical formulas. These formulas do not need the application of the iterative methods, and are not restricted to the high-gain horn designs. The gain of a pyramidal horn is computed without approximating the path length error. Better accuracy with respect to the previous design methods is obtained for various pyramidal horn design examples.