  We reanalyze the problem of the cosmological constant associated with the
phase transition in a self-interacting scalar theory. It is pointed out that
the generally accepted ``triviality'' of $(\lambda\Phi^4)_4$ implies a
first-order phase transition. As a consequence, Spontaneous Symmetry Breaking
can be consistent with zero cosmological constant if one assumes that it
vanishes in the symmetric phase $<\Phi>=0$.
