  Let $K$ be a number field and $\phi\in K(z)$ a rational function. Let $S$ be
the set of all archimedean places of $K$ and all non-archimedean places
associated to the prime ideals of bad reduction for $\phi$. We prove an upper
bound for length of finite orbits of $\phi$ in $\mathbb{P}_1(K)$ depending only
on the cardinality of $S$.
