  We apply the relative weights method to SU(3) gauge theory with staggered
fermions of mass 695 MeV at a set of temperatures in the range $151 \le T \le
267$ MeV, to obtain an effective Polyakov line action at each temperature. We
then apply a mean-field method to search for phase transitions in the effective
theory at finite densities. The result is a transition line in the plane of
temperature and chemical potential, with an endpoint at high temperature, as
expected, but also a second endpoint at a lower temperature. We cannot rule out
the possibilities that a transition line reappears at temperatures lower than
the range investigated, or that the second endpoint is absent for light quarks.
