  The main aim of this paper is to establish the connection between well-known
criteria for the pseudocontinuability of a non-inner Schur function Theta in
the unit disk. In a canonical way we associate a probability measure mu on the
unit circle with Theta. One of the two criteria will be reformulated in the
face of mu, whereas the other one is drafted in view of a completely
non--unitary contraction T having Theta as its corresponding characteristic
function. Our main result clarifies an immediate connection between the
above-mentioned two criteria. For this reason, we construct a special
orthogonal basis in the space of square-integrable functions with respect to mu
and rewrite these criteria in terms of this orthogonal basis.
