A new method for overcoming signal cancellation problems due to correlated interferences which occur in a minimum variance distortionless response beamformer is proposed. Instead of decorrelating the correlated interferences, the coherently combining signal-to-interference plus noise ratio (CC-SINR) beamformer regards them as replicas of the desired signal and coherently combines them with the desired signal. This method uses an eigenvector constraint that suppresses only noise and uncorrelated interferences but retains the desired signal and correlated interferences. The CC-SINR beamformer does not require any preliminary information on correlated interferences. The signal-to-interference plus noise ratio (SINR) of the proposed beamformer output was compared to that of a conventional SINR beamformer when correlated interference, uncorrelated interference, and white noise exist. In addition, various key parameters that affect the performance of the beamformer, such as signal-to-noise ratio, uncorrelated interference-to-noise ratio, angular separation between signals, attenuation factor, phase delay of correlated interference, and the number of sensors were analyzed. All of the experimental results were in good agreement with the analytical results.