  Let $A$ be a H\"older continuous cocycle over a hyperbolic dynamical system
with values in the group of diffeomorphisms of a compact manifold $M$. We
consider the periodic data of $A$, i.e., the set of its return values along the
periodic orbits in the base. We show that if the periodic data of $A$ is
bounded in Diff$^{\,q}(M)$, $q>1$, then the set of values of the cocycle is
bounded in Diff$^{\,r}(M)$ for each $r<q$. Moreover, such a cocycle is
isometric with respect to a H\"older continuous family of Riemannian metrics on
$M$.
