Lattice formulation of finite baryon density QCD is problematic from the co
mputer simulation paint of view; it is well known that for light quark mass
es the reconstructed partition function fails to be positive in a wide regi
on of parameter space. For a large bare quark mass, problems related to the
phase of the determinant are still present but restricted to a small regio
n in the chemical potential mu. We present evidence for a transition line t
hat, starting from the temperature critical point at mu = 0, moves towards
a smaller beta with increasing mu.