Let $X$ be a smooth complex projective variety of dimension $n$ and $\mathcal{L}$ an ample line bundle on it. There is a well known bijective correspondence between the isomorphism classes of polystable vector bundles $E$ on $X$ with $c_{1}(E) = 0 = c_{2}(E) \cdot c_{1} \mathcal (L)^{n−2}$ and the equivalence classes of unitary representations of $\pi_{1}(X)$. We show that this bijective correspondence extends to smooth orbifolds.
