  We carry out a linear stability analysis of a magnetized relativistic
rotating cylindrical jet flow using the approximation of zero thermal pressure.
We identify several modes of instability in the jet: Kelvin-Helmholtz, current
driven and two kinds of centrifugal-buoyancy modes -- toroidal and poloidal.
The Kelvin-Helmholtz mode is found at low magnetization and its growth rate
depends very weakly on the pitch parameter of the background magnetic field and
on rotation. The current driven mode is found at high magnetization, the values
of its growth rate and the wavenumber, corresponding to the maximum growth,
increase as we decrease the pitch parameter of the background magnetic field.
This mode is stabilized by rotation, especially, at high magnetization. The
centrifugal-buoyancy modes, arising due to rotation, tend also to be more
stable when magnetization is increased. Overall, relativistic jet flows appear
to be more stable with respect to their non-relativistic counterpart.
