Remarks on the Cosmological Constant and the $\lambda\Phi^4$ Phase Transition

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 $<\Phi>=0$.