  Let $K$ denote a number field and a finite set $S$ of places of $K$ and
$\phi:\PP^n\rightarrow\PP^n$ be rational morphism defined over $K$. The main
result of this paper proves that there are only finitely many twists of $\phi$
defined over $K$ which have good reduction at all places outside $S$. This
answers a question of Silverman in the affirmative.
