  This paper studies the relationship between Serre's condition $(\R_n)$ and
Auslander--Buchweitz's maximal Cohen--Macaulay approximations. It is proved
that a Gorenstein local ring satisfies $(\R_n)$ if and only if every maximal
Cohen--Macaulay module is a direct summand of a maximal Cohen--Macaulay
approximation of a (Cohen--Macaulay) module of codimension $n+1$.
