This paper presents recent advances in the design of constant H-plane beamwidth horns. The theory of constant H-plane beamwidth horns is discussed and the relationship between aperture size and beamwidth is summarised. The expression for the beamwidth in terms of the H-plane flare angle is shown to be given by a simple formula. A new feed arrangement is described which possesses good vswr properties over at least a 3 to 1 bandwidth.