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The effect of an electromagnetic band-gap (EBG) ground plane on the far-field of the higher order modes of printed antennas, is presented. The performance of the second- and third-order mode of a pair of triangular printed patches with and without an EBG ground plane was studied. It was proved that when the resonance frequency of the EBG is equal or very close to the resonance frequency of one of the higher modes, the entire structure produces fields of high directivity level, with maximum at the broadside and an almost uniform distribution in an area around this direction, which is wider than that produced by the first mode. Therefore, the antenna would operate as a dual-frequency band radiator with similar radiation patterns.