We present a method to compute the density of states induced by a finite density of non magnetic impurities in a d-wave superconductor, in the unitary limit of very strong scattering centers. For frequencies very small as compared to the superconducting gap (ω ≪ ∆ 0 ) the additional density of states has the leading divergence δρ(ω) ≃ n i / |2ω| ln 2 |ω/∆ 0 | . This result is non perturbative.78.20. Ls, 47.25.Gz, 76.50+b, 72.15.Gd Typeset using REVT E X 1