It is known that every ${ \rm C}^r$-orbifold, $1\leq r\leq\infty$, has a compatible ${ \rm C}^s$-differential structure, for every $s$, where $r< s\leq\omega$. We prove that if two reduced ${ \rm C}^r$-orbifolds, $2\leq r\leq\omega$, are ${ \rm C}^2$-diffeomorphic, then they are ${ \rm C}^r$-diffeomorphic. It follows that the compatible ${ \rm C}^s$-differential structure on a reduced ${ \rm C}^r$-orbifold, $2\leq r<s\leq\omega$, is unique up to a ${ \rm C}^s$-diffeomorphism.
Categories: math.GT