  We study the instability of a dusty simple shear flow where the dust
particles are distributed non-uniformly. A simple shear flow is modally stable
to infinitesimal perturbations. Also, a band of particles remains unaffected in
the absence of any background flow. However, we demonstrate that the combined
scenario -- comprising a simple shear flow with a localised band of particles
-- can exhibit destabilisation due to their two-way interaction. The
instability originates solely from the momentum feedback from the particle
phase to the fluid phase. Eulerian-Lagrangian simulations are employed to
illustrate the existence of this instability. Furthermore, the results are
compared with a linear stability analysis of the system using an
Eulerian-Eulerian model. Our findings indicate that the instability has an
inviscid origin and is characterised by a critical wavelength below which it is
not persistent. We have observed that increasing particle inertia dampens the
unstable modes, whereas the strength of the instability increases with the
strength of the coupling between the fluid and particle phases.
