Abstract: The regions with shear stress and mean velocity gradient of opposite sign often exist in complex turbulent shear flows. In these cases, the eddy viscosity hypothesis break down. Hinze regarded the departure from eddy viscosity hypothesis as a result from transportation of mean momentum over distance by the large structures and arrived at a shear stress expression including the second order derivatives of the mean velocity. However, he gave correct results only qualitatively. The present author investigated the expression further and found it greatly over-estimated the shear stress. This means that the flow particles is unlikely to have enough memory of the mean momentum over distance. By assuming the departure from eddy viscosity hypothesis as a result from transportation of shear stress contained in smaller eddies over distance by the large structures, the present author arrived at a new shear stress expression The shear stress estimated so far were in good agreement with the experiment.