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A novel robust adaptive beamformer with new constraints on array magnitude response is proposed. The constraints on array magnitude are non-convex. This problem is solved by exploiting the symmetric array structure. With conjugate-symmetric array weight, the constraints on the array magnitude response is derived as linear constraints. The advantage of the proposed method is that arbitrary width of the array robust response region is available. Even the constraints on the conjugate-symmetric structure of array weight consume some degrees of freedom (DOFs), from the numerical results, it is shown that the array still has very high output signal-to-interference-plus-noise ratio (SINR).