The stability of a streaming magnetized fluid jet penetrated internally by tangential toroidal varying magnetic field is developed based on the linear perturbation technique. The fluid is perfectly conducting, non-viscous and incompressible. The model is acted on by electromagnetic, pressure gradient and inertia forces. The stability criterion is derived and discussed analytically and numerically. The streaming is destabilizing and that influence is independent of the kind of perturbation. The toroidal varying field has no influence on the axisymmetric perturbation while it is stabilizing in the non-axisymmetric modes. The uniform magnetic field outside the jet is stabilizing for all (non-)axisymmetric modes. The electromagnetic force exerts an influence that causes a bending and twisting of the lines of force. For high magnetic field intensity and slow streaming speed, the model unstable states could be shrinked, suppressed and stability sets in.