  In this paper, we describe the results of three-dimensional relativistic
magnetohydrodynamic simulations aimed at probing the role of regular magnetic
field on the development of the instability that accompanies recollimation of
relativistic jets. In particular, we studied the recollimation driven by the
reconfinement of jets from active galactic nuclei (AGN) by the thermal pressure
of galactic coronas. We find that a relatively weak azimuthal magnetic field
can completely suppress the recollimation instability in such jets, with the
critical magnetisation parameter $\sigma_{cr} < 0.01$. We argue that the
recollimation instability is a variant of the centrifugal instability (CFI) and
show that our results are consistent with the predictions based on the study of
magnetic CFI in rotating fluids. The results are discussed in the context of
AGN jets in general and the nature of the Fanaroff-Riley morphological division
of extragalactic radio sources in particular.
