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).