The Influence of the magnetic properties of the liquid on the type of instability (absolute or convective) is investigated for a current-carrying jet. For high values of the Weber number, the instability type is determined by the combination of the capillary instability and the electrical instability due to the current; the boundary between the domains of different instability type is almost not affected by the magnetic properties of the liquid. For small values of the Weber number, a higher value of the magnetic permeability of the liquid can reduce or enlarge the domain of convective instability.