Let us consider a real quadratic-like germ $f_$∗ which is infinitely
renormalizable with tripling essentially bounded combinatorics and
consider the lamination given by the hybrid classes in the
space of quadratic-like germs, then its holonomy map is shown to be $C^1$ at
$f_$∗ if the combinatorics of $f_$∗ satisfies a growth
condition. As a consequence, a proof of the self-similarity of the
Mandelbrot set for this type of combinatorics is given.