  We study the stability of a compressible magnetic plane Couette flow and show
that compressibility profoundly alters the stability properties if the magnetic
field has a component perpendicular to the direction of flow. The necessary
condition of a newly found instability can be satisfied in a wide variety of
flows in laboratory and astrophysical conditions. The instability can operate
even in a very strong magnetic field which entirely suppresses other MHD
instabilities. The growth time of this instability can be rather short and
reach $\sim 10$ shear timescales.
