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As well known, the far-field radiation pattern (RP) of a horn antenna is defined by the amplitude and phase distribution of the field sources at the aperture of the horn angular opening. In turn, this is defined by the excitation and boundary conditions for the field on the horn walls. The possibilities of their changing are quite limited, therefore it is technically difficult to change RP of the horn antennas. Meanwhile, in practice it is often required to have RP, for instance, with very low sidelobe level, low level of the sidelobe in a definite angular sector, etc. There are also arisen the synthesis problems of the RP with the main beam leaf of the table-like form, for instance, for providing the maximum of the coefficient of the area use of a reflector antenna.