Summary: Turbulent boundary layers with convergent and divergent external streamlines over a flat plate in the neighbourhood of a plane of symmetry have been computed using a finite-difference method based on streamline coordinates. While the results for the divergent case are generally satisfactory, error growth has been observed for the convergent flowfield. This is most pronounced near the lateral boundary of the computational domain, but also occurs in the plane of symmetry. As an ad- hoc engineering solution, a modified and more restrictive definition of the domain of dependence is proposed, which eliminates the part of the computational domain where the largest error growth occurs. The observed tendency to instability in the convergent case is confirmed by a simplified stability analysis after von Neumann of the uncoupled governing equations.