A new method of broadband minimum variance beamforming is presented for use with microphone arrays in a reverberant environment. Conventional broadband algorithms (such as the well-known Frost algorithm) suffer from cancellation of the desired look-direction signal when employed in environments containing interference which is correlated with the desired signal. In this paper, a frequency invariant beamforming structure is used to perform spectral averaging. This reduces the correlation between the desired signal and the interference, thereby eliminating the signal cancellation problem. Such a technique is valuable for speech acquisition using a microphone array, since significant correlated interference will be present due to room reverberation.