The Strebel point is a Teichmüller equivalence class in the Teichmüller space
that has a certain rigidity in the extremality of the maximal dilatation. In this paper,
we give a sufficient condition in terms of the Schwarzian derivative for a Teichmüller
equivalence class of the universal Teichmüller space under which the class is a Strebel
point. As an application, we construct a Teichm üller equivalence class that is a Strebel
point and that is not an asymptotically conformal class.