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We consider a 1D topological superconductor (TSC) constructed by coupling apair of Kitaev's Majorana chains with opposite spin configurations. Such a 1Dlattice model is known to be protected by a $T^2 = -1$ time-reversal symmetry.Furthermore, we consider a modeled Rashba spin-orbit coupling on such a systemof $T^2=-1$ time-reversal symmetric TSC. The Rashba spin-orbit couplingtogether with the chemical potential engineered the phase transitions of theedge states in the system and consequently the number of Majorona's zero-energyedge modes (MZM's) emerging at the edge of the coupled chains. Correspondingly,the topological nature of the system is described by a phase diagram consistingof three different phases. The three phases are characterized by a topologicalwinding number, $\mathcal{W}=1$, $2$ (with one and two MZM's: topologicalphases) and $\mathcal{W}=0$ (devoid of any MZM: trivial insulating phase).

Evolution of Majorona zero-energy edge states in a $T^2 = -1$ symmetry protected 1D topological superconductor with dominant spin-orbit coupling