  The Global Magnetorotational Instability (MRI) is investigated for a
configuration in which the rotation frequency changes only in a narrow
transition region. If the vertical wavelength of the unstable mode is of the
same order or smaller than the width of this region, the growth rates can
differ significantly from those given by a local analysis. In addition, the
non-axisymmetric spectrum admits overstable modes with a non-trivial dependence
on azimuthal wavelength, a feature missed by the local theory. In the limit of
vanishing transition region width, the Rayleigh-centrifugal instability is
recovered in the axisymmetric case, and the Kelvin-Helmholtz instability in the
non-axisymmetric case.
