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A dual-frequency microstrip antenna is presented. The proposed antenna consists of a rectangular radiating patch, the ground, and a periodic offset double-sided parallel-strip line structure that is used as the substrate. The phase constant of the substrate is less than 0 at the frequency of operation, which makes the rectangular microstrip antenna work in different modes, and has two resonant frequencies. Experimental results show that the proposed antenna works at 3.3 GHz and 3.9 GHz.