A fairing system for a horizontal stabilizer of an aircraft and to a process for installing said system, such that the fairing system for the sealing of the horizontal stabilizer and the fuselage of the aircraft includes a primary fairing arranged on the horizontal stabilizer of the aircraft, the primary fairing being solidly connected to the horizontal stabilizer which is in turn trimmable with respect to the fuselage, the fairing system in turn comprising a secondary fairing such that the primary fairing is coupled to the horizontal stabilizer through supports arranged in the direction of the chord of the primary fairing, said supports being located in the outer part of said primary fairing with respect to the fuselage, the secondary fairing being arranged in the outer part of the supports.