The problem considered is that of steady laminar flow of an incompressible polar fluid between two parallel plates, one of which is in motion relative to the second. It is shown that the effective viscosity, defined as the shear stress applied to the plates times the distance between the plates divided by the relative velocity of the plates, depends upon the distance between the plates. That is to say, if the applied shear stress is held constant, then as the plates are moved closer together their relative velocity will become slower. The velocity distribution in the polar fluid will change accordingly. It is also shown that at the two extremes of closely spaced plates and widely spaced plates the Couette flow of a polar fluid coincides with the Couette flow of Newtonian fluids, but the Newtonian fluids are of different viscosities. Experimental evidence for the increased viscosity of real fluids between narrowly spaced parallel plates is cited.