Letbe a given bijective analytic mapping of the circumferenceCof the unit circle onto itself. By the uniformization theorem, there exists an analytic Jordan curve Г with the following property: there are two bijective conformal mappingsF(interior of C→ interior of Г) andG(exterior of C → exterior of Г) such thatfor all. We consider this conformal welding under the assumption thatG(∞) = ∞. Our main result is a relation (Theorem 2) which will allow—at least in certain cases—an estimate of the rotation of Г in terms of the given function Ф.