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In this letter, a circular polarization radiator for a dual-band and dual-polarization horn is designed. The radiator consists of a cylindrical helix excited in the axial mode inside a conical horn. Using a conical horn the antenna gain increases, the sidelobe and backlobe levels decrease. With the cylindrical helix, the antenna has the characteristics of circular polarization and broad bandwidth. This antenna is fed by the coaxial cable, so a quarter turn of the helix parallel to the base plate is added for impedance matching. The aperture field and far field expressions are given. Simulated and measured results for voltage standing wave ratio, gain, axial ratio, and radiation patterns of the helicone are presented and show good agreement.