  Based on the quasiconformal theory of the universal Teichm\"uller space, we
introduce the Teichm\"uller space of diffeomorphisms of the unit circle with
$\alpha$-H\"older continuous derivatives as a subspace of the universal
Teichm\"uller space. We characterize such a diffeomorphism quantitatively in
terms of the complex dilatation of its quasiconformal extension and the
Schwarzian derivative given by the Bers embedding. Then, we provide a complex
Banach manifold structure for it and prove that its topology coincides with the
one induced by local $C^{1+\alpha}$-topology at the base point.
