Abstract: A reconfigurable zonal beam forming system for an antenna on a satellite in orbit includes, in cascade, a signal splitter applying signals of equal amplitude to each channel, first variable phase-shifters and amplifiers and a Butler matrix the outputs of which are connected via second variable phase-shifters to the radiating source elements of the antenna. Varying the phase-shifts introduced by the first and second phase-shifters reconfigures the transmitted beam optimally. A preferred variant of the system further includes variable attenuators. A control device is used to apply optimization parameters. A method of optimizing the resulting configuration uses a gradient search algorithm.