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Horn antennas with high directivity or high aperture efficiency are required as feed horns in multibeam reflector antennas and as an element in limited scan arrays. Candidate high directivity horns for circular polarization often suffer from limited bandwidth, complex design or limited aperture size. In this paper a relatively simple dielectric-loaded hybrid mode horn with high efficiency under balanced hybrid conditions (low cross-polarization) is presented. The horn meets the so-called hard boundary conditions, supporting a TEM mode inside the horn at the design frequency. Like other hybrid mode horns this horn is not limited in aperture size, and works for linear and circular polarization. The concept also allows for the design of any boundary conditions between soft and hard.