The invention relates to a method for operating a synchronous machine, comprising the following steps: determining a difference value between the rotor inductance of the synchronous machine in the polar axis direction and the rotor inductance of the synchronous machine in the pole-gap direction for each of a plurality of different 2-tuples from values of useful current adjusted in the rotor-fixed coordinate system of the synchronous machine; preparing a characteristic diagram for the determined difference values in dependence on the 2-tuples of the values of useful current; determining a torque-dependent operating-point trajectory for the 2-tuples of the values of useful current taking into account the magnitude of the determined difference values along the operating-point trajectory to be determined; and operating the synchronous machine according to the determined operating-point trajectory.