  A global mode is shown to be unstable to non-axisymmetric perturbations in a
differentially rotating Keplerian disk containing either vertical or azimuthal
magnetic fields. In an unstratified cylindrical disk model, using both global
eigenvalue stability analysis and linear global initial-value simulations, it
is demonstrated that this instability dominates at strong magnetic field where
local standard MRI becomes stable. Unlike the standard MRI mode, which is
concentrated in the high flow shear region, these distinct global modes (with
low azimuthal mode numbers) are extended in the global domain and are Alfv\'en
continuum driven unstable modes. As its mode structure and relative dominance
over MRI is inherently determined by the global spatial curvature as well as
the flow shear in the presence of magnetic field, we call it the
magneto-curvature (magneto-spatial-curvature) instability. Consistent with the
linear analysis, as the field strength is increased in the nonlinear
simulations, a transition from a MRI-driven turbulence to a state dominated by
global non-axisymmetric modes is obtained. This global instability could
therefore be a source of nonlinear transport in accretion disks at higher
magnetic field than predicted by local models.
