  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.
