  We consider the Stokes problem in an exterior domain $\Omega \subset \R^n$
with an external force $\bbf \in L^s(0,T; \bW^{k,\, r}(\Omega ))\, (k\in \N,
1<r<\infty)$. In the present paper we show that in contrast to $\bu$ the
boundary regularity of the pressure can be improved according to the
differentiability of $\bbf$ up to order $ k$. In particular, this implies that
the pressure is smooth with respect to $x\in \Omega$ if $\bbf$ is smooth with
respect to $x\in \Omega $.
