  We analyze properties of unstable vacuum states from the point of view of the
quantum theory. In the literature one can find some suggestions that some of
false (unstable) vacuum states may survive up to times when their survival
probability has a non-exponential form. At asymptotically late times the
survival probability as a function of time $t$ has an inverse power--like form.
We show that at this time region the energy of the false vacuum states tends to
the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. This means
that the energy density in the unstable vacuum state should have analogous
properties and hence the cosmological constant $\Lambda = \Lambda (t)$ too. The
conclusion is that $\Lambda$ in the Universe with the unstable vacuum should
have a form of the sum of the "bare" cosmological constant and of the term of a
type $1/t^{2}$: $\Lambda(t) \equiv \Lambda_{bare} + d/ t^{2}$ (where
$\Lambda_{bare}$ is the cosmological constant for the Universe with the true
vacuum).
