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A study of an innovative antenna based on split ring resonators (SSRs) is presented. SSRs have been exhaustively used in the literature as the unit cell of periodic structures for obtaining left-handed media, whose interesting characteristics can be applied to waveguides or antennas. In this work, the authors propose the use of only one unit cell of a double SRR as a radiator. The double SRR is printed on a grounded dielectric slab, acting as the radiating element of a microstrip patch antenna, and grounded pins are used to short-circuit the structure for size reduction. A compact dual band antenna is obtained in this way. For example, a particular design making use of PP (εr = 2.2) as substrate allows a size of 0.05 λ0 x 0.05 λ0 for the lower frequency of operation with an acceptable radiation efficiency. Simulated and measured results of return losses, gain and radiation efficiency of this new type of patch antenna are provided.