Charging effects in small tunnel junctions are studied via a transformation which, following Wilson, allows us to treat the hybridization between the two sides and the charging energy exactly. The two conduction bands are transformed to the so-called "hopping" Hamiltonian. The transformation makes the model suitable for a full renormalization group calculation. Here we study a simplified version of this Hamiltonian. We keep only the first term that hybridize directly the two bands and which involves the charging energy and the junction coupling strength. The resulting four level system is solved exactly and the eigenvalues, the meansquare charge difference, and the charge transfer fluctuations are calculated.