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A novel asymmetrical antenna with a high level of signal rejection at 3.3-3.6 and 5.15-5.825-GHz is proposed for ultra-wideband applications. The CPW-fed antenna consists of a ground plane with a circular slot on one layer and a circular radiator on the other layer. Compared with symmetrical antennas, the radiator is moved by an offset distance from the centre of the structure. This design features the advantage of alleviating the requirement on the space for band-rejected elements. The improved band-notched performance is obtained by utilising a combination of three-quarter-wavelength band-rejected elements. Both simulated and measured results are demonstrated and discussed to validate the design.