  We derive new stability criteria for purely MHD instabilities in rotating
jets, in the framework of the ballooning ordering expansion. Quite
unexpectedly, they involve a term which is linear in the magnetic shear. This
implies that cylindrical configurations can be destabilized by a negative
magnetic shear as well as by a favorable equilibrium pressure gradient, in
distinction with the predictions of Suydam's stability criterion, which
suggests on the contrary that the shear is always stabilizing.
  We have used these criteria to establish sufficient conditions for
instability. In particular, the magnetic shear can always destabilize jets with
vanishing current density on the axis, a feature which is generically found in
jets which are launched from an accretion disk. We also show that standard
nonrotating jet models (where the toroidal field dominates the poloidal one),
which are known to be unstable, are not stabilized by rotation, unless the
plasma $\beta$ parameter and the strength of the rotation forces are both close
to the limit allowed by the condition of radial equilibrium.
  The new magnetic shear-driven instability found in this paper, as well as the
more conventional pressure-driven instability, might provide us with a
potential energy source for the particle acceleration mechanisms underlying the
high energy emission which takes place in the interior of AGN jets.
