  We analyze the phase diagram of QCD with four staggered flavors in the (mu,
T) plane using a method recently proposed by us. We explore the region T > 0.7
Tc and mu <1.4 Tc, where Tc is the transition temperature at zero baryon
density, and find a first order transition line. Our results are quantitatively
compatible with those obtained with the imaginary chemical potential approach
and the double reweighting method, in the region where these approaches are
reliable, T > 0.9 Tc and mu < Tc. But, in addition, our method allows us to
extend the transition line to lower temperatures and higher chemical
potentials.
