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The use of dielectric resonator antennas (DRAs) is motivated by their low loss, small size, and their ability to produce unidirectional radiation patterns with small back side radiation. Previously, researchers used one DRA to produce dual band performance when excited by a slot radiator. Consequently, unidirectional patterns are achieved only in one band, which corresponds to the DRA resonance. However, in this paper, two DRAs are fed simultaneously by a coplanar waveguide (CPW) through two slots in the CPW ground plane. Here, the DRAs, not the slots, act as radiators and therefore unidirectional radiation is achieved at both bands. Using the commercial softwares HFSS and CST, the dimensions of the dual antenna are tuned such that the antenna radiates at 4.5 and 6.5 GHz with very good agreement between the two softwares. A full parametric study is carried out.