  We study the stability of compressible cylindrical differentially rotating
flow in the presence of the magnetic field, and show that compressibility
alters qualitatively the stability properties of flows. Apart from the
well-known magnetorotational instability that can occur even in incompressible
flow, there exist a new instability caused by compressibility. The necessary
condition of the newly found instability can easily be satisfied in various
flows in laboratory and astrophysical conditions and reads $B_{s} B_{\phi}
\Omega' \neq 0$ where $B_{s}$ and $B_{\phi}$ are the radial and azimuthal
magnetic fields, $\Omega' =d \Omega/ds$ with $s$ being the cylindrical radius.
Contrary to the magnetorotational instability that occurs only if $\Omega$
decreases with $s$, the newly found instability operates at any sign of
$\Omega'$. The considered instability can arise even in a very strong magnetic
field that suppresses the magnetorotational instability.
