  We perform a linear analysis of the stability of a magnetized relativistic
non-rotating cylindrical flow in the aproximation of zero thermal pressure,
considering only the m = 1 mode. We find that there are two modes of
instability: Kelvin-Helmholtz and current driven. The Kelvin-Helmholtz mode is
found at low magnetizations and its growth rate depends very weakly on the
pitch parameter. The current driven modes are found at high magnetizations and
the value of the growth rate and the wavenumber of the maximum increase as we
decrease the pitch parameter. In the relativistic regime the current driven
mode is splitted in two branches, the branch at high wavenumbers is
characterized by the eigenfunction concentrated in the jet core, the branch at
low wavenumbers is instead characterized by the eigenfunction that extends
outside the jet velocity shear region.
