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The beamwidth of a linear array decreases as frequency increases. For wideband beamformers such as microphone arrays intended for teleconferencing, this frequency dependence implies that signals incident on the outer portions of the main beam are subject to the undesirable effects of lowpass filtering. In this paper we discuss several ways of attaining beamwidth constancy and present a novel method based on superimposing several marginally steered beams to form a constant beamwidth multi-beam. This method provides an analytically tractable framework for designing constant beamwidth beamformers.