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In this work, we show that a quasi-one-dimensional $d_{x^2-y^2}$-wavesuperconductor with Rashba spin-orbit coupling is a DIII class, time-reversalinvariant, topological superconductor (TS) which supports a Majorana KramersDoublet (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 fieldbreaks TRS and drives the system from DIII to D class in which case a singleMES appears at each end of the TS. We show that a MKD induces resonant Andreevreflection with zero bias conductance peak of $4e^2/h$. Experimentalrealizations of the proposed model are discussed.

Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling