Results are presented on the linear stability of the collisionless $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ mode in a dense Z pinch. It is shown that a reduction in growth rate by a factor of about 10 (when compared to the zero Larmor radius result) is possible by initializing the Z pinch with a sufficiently low line density. With the completion of this work we conclude that linear, large Larmor radius effects cannot stabilize the high temperature, dense Z pinch. Such pinches will always exhibit linear $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ or $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ instabilities with growth times comparable to the radial Alfv\'en transit time.