  Let $R$ be a commutative Noetherian ring and $E$ the minimal injective
cogenerator of the category of $R$-modules. An $R$-module $M$ is (Matlis)
reflexive if the natural evaluation map $M \to
\operatorname{Hom}_R(\operatorname{Hom}_R(M,E),E)$ is an isomorphism. We prove
that if $S$ is a multiplicatively closed subset of $R$ and $M$ is a reflexive
$R$-module, then $M$ is a reflexive $R_S$-module. The converse holds when $S$
is the complement of the union of finitely many minimal primes of $R$, but
fails in general.
