  We present a canonical approach to study properties of QCD at finite baryon
density rho, and apply it to the determination of the phase diagram of
four-flavour QCD. For a pion mass of about 350 MeV, the first-order transition
between the hadronic and the plasma phase gives rise to a co-existence region
in the T-rho plane, which we study in detail. We obtain accurate results for
systems containing up to 30 baryons and quark chemical potentials mu up to 2T.
Our T-mu phase diagram agrees with the literature when mu/T < 1. At larger
chemical potential, we observe a ``bending down'' of the phase boundary. We
characterise the two phases with simple models: the hadron resonance gas in the
hadronic phase, the free massless quark gas in the plasma phase.
