  We consider the class of meromorphic univalent functions having a simple pole
at $p\in(0,1)$ and that map the unit disc onto the exterior of a domain which
is starlike with respect to a point $w_0 \neq 0,\, \infty$. We denote this
class of functions by $\Sigma^*(p,w_0)$. In this paper, we find the exact
region of variability for the second Taylor coefficient for functions in
$\Sigma^*(p,w_0)$. In view of this result we rectify some results of James
Miller.
