Abstract. In this note, we give a direct self-contained proof of the Schur parametrization of all contractive intertwining liftings of an intertwining contraction. The original part of the proof resides in the use of the Möbius transform of contractions inspired by [14], Chapter 6.

AMS Subject Classification (1991): 47A20, 47A57

Received June 1, 1995. (Registered under 5697/2009.)