A new functional for the entropy that is asymptotically correct both in the high and low density limits is proposed. The new form is S = S^(id) + S^(ln) + S^(r) + S^(c) where the new term S^(c) depends on the p-bodies density fluctuations α_p and renormalizes the ring approximation S^(r). This result is obtained by analyzing the functional dependence of the most general expression of the entropy: Two main results for S^(c) are proven: i) In the thermodynamic limit it is only a functional of the one body distribution function and ii) by summing to infinite order the leading contributions in the density a new numerical expression for the entropy with a new renormalized ring approximation is obtained. The relation of these results to the incompressible approximation for the entropy is discussed and preliminary numerical results on hard spheres are presented.