In this letter a simple and fast method is presented for improving linear array radiation patterns produced by existing synthesis algorithms. Given a linear aperiodic array with elements lying at specified positions, having uniform distribution of the excitations and radiating a pencil beam {in the broadside direction}, the proposed approach iteratively modifies the positions of the elements in order to reduce the power radiated in the sidelobe region. Numerical examples show the effectiveness of the method, and the effects of sidelobe power reduction on other parameters of the antenna are examined.