A novel type of multihole directional coupler is presented as well as a design method involving novel procedures. The device couples two orthogonal TE11 modes in a circular waveguide into two orthogonal TE21 modes with specified excitations in a surrounding coaxial waveguide, which has the circular waveguide as inner conductor. A simple, novel analytical procedure is used to determine azimuthal hole positions, such that each of the input modes couples to only the desired coaxial TE21 mode. The method is applied to a specific coupler which is designed to couple −14 dB to both higher-order coaxial modes in the band from 10 GHz to 14 GHz. The suppression of undesired modes is generally better than 40 dB. The coupler is intended for broadband, dual-polarized matched feeds, which are able to compensate the intrinsically high cross polarization of offset single reflector antenna systems.