A fairing for streamlining the junction between the horizontal stabilizer and the fuselage or the fin of an aircraft, comprising an upper fairing shell, a lower fairing shell, a leading edge extension, and several fittings to join the upper and lower fairing shells to the horizontal stabilizer. The upper and lower fairing shells are solid laminates of composite material that are designed with a shape, composition, and thickness such that they can be elastically deformed when they are fitted to the horizontal stabilizer, providing a contact force permitting them to lay permanently in contact with the fuselage or fin. A process for manufacturing the fairing shells.