We consider the class of meromorphic univalent functions having a simple pole at <img border=0 width=111 height=19 src="http://fbpe/img/cubo/v12n1/img7.jpg">and that map the unit disc onto the exterior of a domain which is starlike with respect to a point <img border=0 width=123 height=21 src="http://fbpe/img/cubo/v12n1/img5.jpg">. We denote this class of functions by <img border=0 width=108 height=23 src="http://fbpe/img/cubo/v12n1/img6.jpg">. In this paper, we find the exact region of variability for the second Taylor coefficient for functions in <img border=0 width=104 height=22 src="http://fbpe/img/cubo/v12n1/img6.jpg">. In view of this result we rectify some results of James Miller.