A method and arrangement for reducing the torque ripple of a brushless DC motor having a stator, a rotor, and a motor control unit, via which motor control unit the motor is controlled in a polyphase manner, having a data memory for storing rotational angle-dependent correction data of the control current of the motor, which are impressed on the instantaneous values for controlling the motor. In a first step, for each position of the rotor, the phase currents holding the rotor in this position are determined and are used to derive reference current data, which is stored in a table of the data memory together with the respective position data of the rotor, determined by the position sensor. In a second step, during continuous operation of the motor, the position-dependent reference current data stored in the data memory is combined with the control current of the motor.