Cogging torque in flux-switching permanent magnet (FSPM) machines dominates the whole torque ripples due to its special doubly salient structure and high air-gap PM flux density. In this study, the chamfering method of right angles is utilised in both stator and rotor sides of FSPM machines to suppress the cogging torque. First, an analytical expression of cogging torque, taking the influence of the introduced right angles into consideration, is derived. On the basis of the derived model, the optimal dimensions of right angles are obtained and verified by both finite element analysis and experiments. Besides, the impacts of the proposed technique on phase electro-motive force and electromagnetic torque are also evaluated. The predicted results indicate that the proposed technique can significantly reduce cogging torque in FSPM machines with negligible reduction of average torque.