  The tricritical line of the first-order chiral phase transition is
investigated in the U(Nf)xU(Nf) sigma model by means of the ring improved
one-loop finite temperature effective potential. To locate the tricritical line
in the space of the coupling constants, we expand the effective potential up to
third order in the high temperature expansion, and up to sixth order in the
order parameter expansion. In this approximation, the tricritical line can be
evaluated to the lowest order of the coupling constants and it follows an
analytic relation between the tree-level masses of the scalar bosons. The
validity of the high temperature expansion, the order parameter expansion, and
the ring improved perturbation is critically examined. This result does not
alter if one includes the massless fermions with the small Yukawa couplings.
