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A new method for sum and difference beam pattern synthesis with Iow sidelobe is proposed. In the situation of phase taper weighting, it makes use of Fourier transform pair relationship existing between the array factor and the element excitations and uses a loop iterative way to derive the array element excitations according to given array factor. The iteration does not stop until the array element excitations meet the initial sidelobe requirements. The method overcomes the defects of traditional methods, such as more searching times, larger amount of calculation and poor robustness. In addition, it can also synthesize the low sidelobe pattern in case of element failures. Simulation verifies the effectiveness of the method.