  In this work, we show that a quasi-one-dimensional $d_{x^2-y^2}$-wave
superconductor with Rashba spin-orbit coupling is a DIII class, time-reversal
invariant, topological superconductor (TS) which supports a Majorana Kramers
Doublet (MKD) at each end of the TS. A MKD is a pair of Majorana end states
(MESs) protected by time-reversal symmetry (TRS). An external magnetic field
breaks TRS and drives the system from DIII to D class in which case a single
MES appears at each end of the TS. We show that a MKD induces resonant Andreev
reflection with zero bias conductance peak of $4e^2/h$. Experimental
realizations of the proposed model are discussed.
