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The concept of achieving a dual-band antenna with two different radiation patterns using a single cylindrical dielectric resonator is presented. Both simulated and experimental measured results are conducted to prove the validity of the proposed concept. A broadside circularly-polarized pattern with 7% bandwidth and a vertically polarized omnidirectional pattern with 17.3% bandwidth are obtained, simultaneously. The minimum measured axial ratio is found to be 1.3 dB. The front-to-back ratio is measured to be 15 dB. A design suitable for both Global Positioning System and wireless local area network applications is proposed.