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Dual band antennas are important in communication systems which operate in more than one frequency band. This paper presents a new dual band coplanar waveguide-fed-slot coupled rectangular dielectric resonator antenna operating at the two frequency bands centered at 5.4 and 6.8 GHz. The use of DR allows for unidirectional radiation with a front to back ratio of more than 10 dB. The designed antenna is linearly polarized with a cross polarization level more than 26 dB lower than the co-polarization level.