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A new approach for the synthesis of thinned uniformly spaced linear arrays featuring a minimum sidelobe level is presented. The method is based on the iterative Fourier technique to derive element excitations from the prescribed array factor using successive forward and backward Fourier transforms. Array thinning is accomplished by setting the amplitudes of the largest element excitations to unity and the others to zero during each iteration cycle. The number of turned on elements depends on the array filling factor and the total count of element positions. The effectiveness of the new method will be demonstrated for various 200-element linear arrays and compared with published results.