The Kelvin-Helmholtz instability in sheared magnetohydrodynamic flow of an ideally conducting rotating inhomogeneous compressible plasma is investigated. The asymptotic behaviour inx of the Kelvin-Helmholtz eigenfunctions for the case of finite compressibility in the presence of rotation is discussed and instability condition is derived. In the incompressible limit, a dispersion relation is derived which has been solved numerically and discussed in detail. It is found that the inhomogeneous system is unstable in an incompressible plasma.
