The concept and development of a highly efficient pyramidal horn is described. The radiating element comprises a rectangular radiating aperture fed by two smaller flared square wave guide sections via a bifurcated H-plane surface discontinuity. For the simultaneous feeding of the two-port radiating element, the total antenna includes a compact H-plane power divider. Properly weighted TEn0 modes (n is an element of N*) are excited at the output of the two flared waveguide sections. The bifurcation is responsible for the recombination of the incoming fields. The low-dispersive modal coupling coefficients (or transmission coefficients of the bifurcation's generalized scattering matrix) between the excitation and the aperture modes enable the broadband realization of the targeted aperture modal content. The common wave guide section is responsible for the phase alignment of the aperture modes. The design method targets a preoptimized model, which approximates the amplitude of the aperture modes TEm0 (m = 1, 3, 5,...) in the order of 1/ m and minimizes the irrelative phase difference. Finally, maximum aperture efficiency can be achieved by fine tuning and with low computational complexity. Design principles are given and illustrated by means of an example involving an antenna with aperture size of about 2.8 lambda(0) x 1.4 lambda(0) (lambda(0) is the free-space wavelength at the central frequency of operation). The antenna exhibits aperture efficiency levels above 95% over the entire Ku-Tx-b and (10.7-12.75 GHz), as well as a compact profile (4.1 lambda(0)). The measured results of a prototype manufactured through milling verify experimentally the numerically predicted performance.