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A compact CPW-fed microstrip antenna is proposed. The structure consists of a square patch with Koch boundary and triangle slots. Also, the antenna resonates at two distinct frequencies. The simulated results establish that the dual-band is due to the triangle slots and the lower due to the Koch boundary. The proposed antenna gives bidirectional pattern in the E plane and omnidirectional radiation pattern in the H plane over its almost whole frequency band of interest. In the article, some parametric studies on the effect of the antenna on return loss are done. One can conclude that the designed antenna could be used for a variety of wireless services.