A recent paper by \textit{J. S. Bramley} and \textit{D. M. Sloan} [Comput. Fluids 15, 297-311 (1987; Zbl 0626.76040)] describes a numerical solution for two-dimensional flow of a viscous, incompressible fluid in a branching channel. A grid generation algorithm was used to map the solution region onto a rectangle and an upwind finite difference scheme was then used to solve the Navier-Stokes equations in terms of stream function and vorticity. Here we extend the earlier work by describing an efficient solution of the problem using a nonlinear multigrid algorithm. Of particular interest is the treatment of the boundary conditions in a manner which does not destroy the interior smoothness in the neighbourhood of the boundary.