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tokens: points also remain almost unchanged. Further investigation of stabilizing effects due to increasing magnetic field strength will be discussed in Section 6. Let us compare the stability of relativistic magnetized jets with their non-relativistic counterparts. Fig. 8 shows the non-relativistic stability analysis of the strongly magnetized jet. Fig. 8 of this paper is borrowed from Kim etal. (2015) , where it was labelled Fig. 5 . We can directly compare Fig. 6 with Fig. 8 (a). We see that the fundamental pinch mode in Fig. 6 (a) for the mildly relativistic ( 0 2) case is slightly more stable than the fundamental pinch mode in Fig. 8 (a). The growth rate of the fundamental pinch mode even for the mildly relativistic jet is now below the stability criterion. For the first reflection pinch instability mode, the growth rate at resonance (the wavenumber where its growth rate is a maximum) has a slightly lower value. However, the difference is not significant. Figure 8. The dispersion relation of the non-relativistic magnetized jets with 0.1 and M 4. The velocity profile in the jet is top-hat. The plasma of the jet is 1/2. This is obtained in the non-relativistic linear stability analysis that appears in Kim etal. (2015) . Panel (a) shows the pinch mode ( m 0) instabilities, while panel (b) shows the kink mode ( m 1) instabilities. The red and blue lines represent the fundamental and the first reflection mode. The real and imaginary part of are shown as the solid and dashed lines. The dotted curves refer to the stability criterion for each of the unstable modes. Similarly, let us also compare our relativistic results with non-relativistic results for the kink ( m 1) modes. Please compare Fig. 7 with Fig. 8 (b). Actually there are only minor improvements in the stability for the fundamental kink mode of the mildly relativistic jet. For the first reflection mode, there is only a very tiny range of unstable wavelengths in the non-relativistic jet. However, the range is relatively wider in the relativistic jet. 5.2 Scaling property of the strongly magnetized jets Analogously to Section 4.3 , we study the stability of magnetized jets with increasing Lorentz factors. In this section, we use the strongly magnetized jets ( 1/2) to verify that there still exists a scaling law even in the magnetized case. Fig. 9 is analogous to Fig. 5 but for the strongly magnetized jet case. Fig. 9 (a) shows the pinch mode ( m 0) instabilities. In Fig. 9 (a), we can see the same trend that is shown in Fig. 5 (a). The temporal growth rate of the fundamental pinch instability mode is inversely proportional to the square of the Lorentz factor ( I 1/ 0 2 ). The growth rate of the first reflection pinch instability mode, however, is just proportional to 1/ 0 . Figure 9. The scaling property of the strongly magnetized jets ( 1/2) with increasing Lorentz factor. Panel (a) shows the pinch mode ( m 0) instabilities, while panel (b) shows the kink mode ( m 1) instabilities. The red