A method of piloting an aircraft (1) provided with at least one rotary wing (2) and a tail rotor (10) suitable for swiveling to pass reversibly from an anti-torque mode of operation to a propulsion mode of operation, said tail rotor (10) having a plurality of second blades (12) having a second variable pitch and rotating about an axis of rotation (AX), said axis of rotation presenting a first variable salient angle (θ) relative to a first plane (P1). Thus, in the anti-torque mode of operation, said second pitch is controlled using first control means (31). Furthermore, in the propulsion mode of operation, said first salient angle (θ) is controlled using first control means (31) and said second pitch is controlled using second control means (32) for controlling thrust.