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A novel method for sidelobe reduction in phased array antennas is described, using equal-amplitude elements with randomised phase reversals to create an effective taper. Peak sidelobe levels of ¿¿18.8 dB for a 128 element array and ¿¿20.2 dB for 256 elements can be obtained with 9 and 27 phase reversed elements respectively. The associated gain reduction is between 1 and 2 dB. Statistical theory is used to explain the results.