This paper describes a method to reduce cogging torque in permanent magnet (PM) machines by shifting elementary-cogging unit (ECU). The ECU division principle and the feature of cogging torque produced by ECU are also discussed. The proper shift angles for each ECU are deduced according to both fractional and integral slot number per pole, by which any order harmonic cogging torque could be eliminated without the introduction of any new harmonic torque. This paper investigates the validity of the effectiveness of ECU shifting techniques using PM machines with different match of slot number per pole in 2-D finite-element models.