  We consider a 1D topological superconductor (TSC) constructed by coupling a
pair of Kitaev's Majorana chains with opposite spin configurations. Such a 1D
lattice 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 system
of $T^2=-1$ time-reversal symmetric TSC. The Rashba spin-orbit coupling
together with the chemical potential engineered the phase transitions of the
edge states in the system and consequently the number of Majorona's zero-energy
edge modes (MZM's) emerging at the edge of the coupled chains. Correspondingly,
the topological nature of the system is described by a phase diagram consisting
of three different phases. The three phases are characterized by a topological
winding number, $\mathcal{W}=1$, $2$ (with one and two MZM's: topological
phases) and $\mathcal{W}=0$ (devoid of any MZM: trivial insulating phase).
