Method for controlling the electromagnetic torque of a three-phase permanent magnet synchronous machine of a powertrain equipping a motor vehicle, comprising: - measuring the current (I 1, I 2, I 3) delivered on the three phases of the machine, - transposing the three measured currents into a direct current component (I d) and a quadratic current component (I q) using a transform of the three-phase systems, - receiving a setpoint (I q_req) for the quadratic current component (I q) and a setpoint (I d_req) for the direct current component (I d) resulting from a mapping of the optimal direct current component for providing the electromagnetic torque over the entire desired range, - calculating the direct and quadratic components of the non-saturated control voltage (V d_nonsat, V q_nonsat) from the direct and quadratic current components (I d, I q) and the direct and quadratic current setpoints (I d_req, I q_req), - calculating the direct and quadratic components of the saturated control voltage (V d_sat, V q_sat) from the quadratic current component (I q) and the quadratic current setpoint (I q_req), - controlling (190, 200) the output voltages (V 1, V 2, V 3) of an inverter coupled at the input of the synchronous machine using the non-saturated controls if the direct component of the current (I d) is positive, or using the saturated controls if the direct component of the current (I d) is negative, said method being characterized in that it further comprises, before calculating the saturated and non-saturated control voltages, correcting the setpoint (I q_req) of the quadratic current component in accordance with the values of the direct and quadratic components (I d, I q) of the current flowing in the machine and the values of the direct (Ld) and quadratic (Lq) components of the inductance of the synchronous machine, wherein the correcting comprises the prior provision of a mapping of the quadratic current component (I q) providing the desired torque (I qseul) alone, the setpoint of the quadratic current component being corrected using the equation: I qreq = I qseul − I d I q L d − L q Φ ƒ where φf is the flux generated by the magnets of the rotor expressed in weber (Wb), I qseul is the quadratic component of the stator current providing the desired torque alone in the Park plane, I d is the direct component of the stator current in the Park plane, calculated from the measured stator currents, I q is the quadratic component of the stator current in the Park plane, calculated from the measured stator currents, L d is the direct component of the stator inductance in the Park plane, and L q is the quadratic component of the stator inductance in the Park plane. - measuring the current (I 1, I 2, I 3) delivered on the three phases of the machine, - transposing the three measured currents into a direct current component (I d) and a quadratic current component (I q) using a transform of the three-phase systems, - receiving a setpoint (I q_req) for the quadratic current component (I q) and a setpoint (I d_req) for the direct current component (I d) resulting from a mapping of the optimal direct current component for providing the electromagnetic torque over the entire desired range, - calculating the direct and quadratic components of the non-saturated control voltage (V d_nonsat, V q_nonsat) from the direct and quadratic current components (I d, I q) and the direct and quadratic current setpoints (I d_req, I q_req), - calculating the direct and quadratic components of the saturated control voltage (V d_sat, V q_sat) from the quadratic current component (I q) and the quadratic current setpoint (I q_req), - controlling (190, 200) the output voltages (V 1, V 2, V 3) of an inverter coupled at the input of the synchronous machine using the non-saturated controls if the direct component of the current (I d) is positive, or using the saturated controls if the direct component of the current (I d) is negative, where φf is the flux generated by the magnets of the rotor expressed in weber (Wb), I qseul is the quadratic component of the stator current providing the desired torque alone in the Park plane, I d is the direct component of the stator current in the Park plane, calculated from the measured stator currents, I q is the quadratic component of the stator current in the Park plane, calculated from the measured stator currents, L d is the direct component of the stator inductance in the Park plane, and L q is the quadratic component of the stator inductance in the Park plane.