The authors solve the incompressible Navier-Stokes equations in the streamfunction-vorticity formulation on a two-dimensional non-uniform orthogonal grid for the flow in a constricted channel. The grids were generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh, so that the shape of the channel boundary could vary from a smooth constriction to one possessing a very sharp but smooth corner. The governing equations are replaced by a fourth-order central difference scheme, and the solution is obtained through Newton iterations. Extra boundary conditions, necessary for wide-molecule scheme, follow the procedure by \textit{W. D. Henshaw} et al. [Comput. Fluids 23, No. 4, 575-593 (1994; Zbl 0801.76055)]. It has been found by the authors that for the sharpest corner considered, very accurate results have been obtained with errors less than \(5\times 10^{-7}\) for Reynolds number up to 250, and the observed order of the method was close to four, indicating that the method was genuinely fourth-order. This would indicate, using the harmonic mean, about 400 times more accurate calculations than those of the corresponding second-order method. This also implies that, for a specified tolerance, it is possible to reduce the number of nodes by a factor of 4.5 times (when using the fourth-order method) in comparison with a second-order scheme, obtaining also 180 times reduction in CPU time. This reviewer is wondering whether this is also true for computations with primitive variables.