  The loop-expansion of the effective potential in the $O(N)$-symmetric
$\phi^4$-model contains generically two types of large logarithms. To resum
those systematically a new minimal two-scale subtraction scheme $\tMS$ is
introduced in an $O(N)$-invariant generalization of $\MS$. As the $\tMS$ beta
functions depend on the renormalization scale-ratio a large logarithms
resummation is performed on them. Two partial $\tMS$ renormalization group
equations are derived to turn the beta functions into $\tMS$ running
parameters. With the use of standard perturbative boundary conditions, which
become applicable in $\tMS$, the leading logarithmic $\tMS$ effective potential
is computed. The calculation indicates that there is no stable vacuum in the
broken phase of the theory for $1<N\leq 4$.
