The problem dealing with the two-dimensional steady and slow now of an Oldroyd 6-constant fluid between intersecting planes, one of which is fixed and the other moving, has been analysed. Using truncated series expansions given by Strauss  for the stream function and stress components, the governing equations of the problem are reduced to linear ordinary differential equations. These equations have been solved analytically subject to the relevant boundary conditions. The effects of the non-Newtonian parameters on the flow pattern are carefully delineated. There is, unlike the case of Newtonian fluid, a secondary flow near the corner.