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This letter presents the improved cross-polar performance of a matched feed with an offset parabolic reflector antenna of low focal-length-to-diameter (F/D) ratio and higher offset angle. In the pyramidal horn, the higher order mode (TE11) has been added in correct amplitude and phase with respect to the dominant mode (TE01) . Parametric study on the secondary radiation pattern has been carried out for different values of offset angle. The numerical results have been presented on radiation pattern for both linearly polarized and circularly polarized rectangular matched feed. The design of a rectangular matched feed and its simulated secondary patterns have also been included.