  The influence of viscosity gradient (due to shear flow) on low frequency
collective modes in strongly coupled dusty plasma is analyzed. It is shown that
for a well known viscoelastic plasma model, the velocity shear dependent
viscosity leads to an instability of the shear mode. The inhomogeneous viscous
force and velocity shear coupling supply the free energy for the instability.
The combined strength of shear flow and viscosity gradient wins over any
stabilizing force and makes the shear mode unstable. Implication of such a
novel instability and its applications are briefly outlined.
