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This letter presents the design of a dual-mode corrugated matched feed to cancel the unwanted high cross polarization and beam squinting in an offset parabolic reflector antenna. The matched feed concept has been implemented in a cylindrical corrugated structure by adding a higher order HE21 mode to the fundamental HE11 mode. The designed feed was then used to illuminate a linearly, as well as a circularly, polarized offset parabolic reflector antenna, and the secondary radiation patterns were computed. Significant improvement in the cross polarization was observed when the results were compared to that of a conventional corrugated horn illuminated offset reflector antenna.