Is there a 'South Star'?

There is a "South Star" called Sigma Octanis located in the constellation Octans, but it is so dim that virtually nobody calls it the south star.

Just another side note: Polaris doesn't always point North. The reason is that our Earth has a precession effect which make the North pole circulate around the sky. This picture illustrates my point.

EDIT: Just to clarify, the picture is showing the circulation of the south celestial pole around the south ecliptic pole.

EDIT2 : References: http://en.wikipedia.org/wiki/Pole_star#mediaviewer/File:Precession_S.gif
http://en.wikipedia.org/wiki/Pole_star