  We study strong tunneling (i.e. transmission $h/e^2R_T \gg 1$) in the
single-electron box with many transverse modes at zero temperature. We develop
a new renormalization group method which includes all charge states and
requires no initial or final energy cutoff. We determine the ground-state
energy, the average charge and the renormalized charging energy. The covered
range for the coupling constant and the gate voltage is much increased in
comparison to recent perturbative approaches, poor man scaling methods and
Quantum Monte Carlo simulations. We reach the regime where Coulomb blockade
become practically unobservable.
