An aircraft (1) horizontal stabilizer (2) which can vary its sweep angle (6) by rotating around an essentially vertical axis (4) with respect to the direction of flight of the aircraft (1) when the aircraft (1) is in flight at high speeds, close to the speed of sound, this axis (4) being contained in the plane of symmetry of the aforementioned aircraft (1), the aforementioned horizontal stabilizer (2) being is a single and structurally continuous component such that it does not transmit a bending moment to the fuselage (14) structure of the aircraft (1), which permits it to be of reduced weight, such that the horizontal stabilizer (2) rotates in a single way and a single direction around the axis (4) to achieve the sweep angle (6) required for high-speed flight.