  We study the applicability of the {\it parallel tempering method} (PT) in the
investigation of first- order phase transitions. In this method, replicas of
the same system are simulated simultaneously at different temperatures and the
configurations of two randomly chosen replicas can occasionally be
interchanged. We apply the PT for the Blume-Emery-Griffiths (BEG) model, which
displays strong first-order transitions at low temperatures. A precise estimate
of coexistence lines is obtained, revealing that the PT may be a successful
tool for the characterization of discontinuous transitions.
