We here derive the optimum sum and difference beamformers for monopulse target localization using a linear array. The beamformers are constructed, treating as superelements two overlapping subarrays. Removing the common factor associated with the superelement pattern from the angle error function leads to a closed-form target angle estimator independent of any adaptive nulling performed. Performance analysis of the angle estimator is conducted, and a procedure is developed to construct the beamformers, which achieve the minimum estimation variance under Gaussian noise. It is shown that the optimum angle estimator using the maximum overlapping subarrays is efficient for a moderately high signal-noise ratio (SNR) and a small off-boresight angle. The proposed method can be easily modified to incorporate interference cancellation.