We study strong tunneling (i.e. transmission h/e 2 RT ≫ 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.73.23. Hk,73.40.Gk,73.30.Rw Introduction. Metallic nanostructures with junctions of low capacitance show quantization of electric charge and Coulomb blockade phenomena due to large charging energy [1-3]. The simplest system in which one can see Coulomb blockade effects is the single-electron box. Electrons enter or leave a small metallic island via a tunnel junction with many transverse channels. The junction is characterized by a resistance R T and a capacitance C. The charge on the island is controlled by a capacitively (with C G ) coupled external voltage V G . In the "weak tunneling" regime, i.e., when the transmission T = h/e 2 R T of the barrier is much less than unity, the average charge of the box can be described within the "orthodox theory" [1] which treats tunneling in lowest order perturbation theory (golden rule). This means that the energy for charge N on the island is given by the classical expression