We study $C^3$ orientation preserving circle homeomorphisms with irrational rotation number and non-flat critical points. By Yoccoz, two of these maps with same irrational rotation are topologically conjugate. In this talk, we define the Renormalization operator of this kind of maps and assuming some properties of this operator we prove that the conjugacy is a $C^{1+\alpha}$ diffeomorphism, for a total Lebesgue measure set of irrational rotation numbers. Joint work with Pablo Guarino (Universidade Federal Fluminense, Brazil).