We show that stochastically continuous, time-homogeneous affine processes on the canonical state space ℝ^m_{≥ 0} are always regular. In the paper of Duffie et al. (Ann Appl Probab 13(3):984-1053, 2003) regularity was used as a crucial basic assumption. It was left open whether this regularity condition is automatically satisfied for stochastically continuous affine processes. We now show that the regularity assumption is indeed superfluous, since regularity follows from stochastic continuity and the exponentially affine form of the characteristic function. For the proof we combine classic results on the differentiability of transformation semigroups with the method of the moving frame which has been recently found to be useful in the theory of SPDEs.