  Higher-order topological superconductors and superfluids host
lower-dimensional Majorana corner and hinge states since novel topology
exhibitions on boundaries. While such topological nontrivial phases have been
explored extensively, more possible schemes are necessary for engineering
Majorana states. In this paper we propose Majorana corner states could be
realized in a two-dimensional attractive quantum spin-Hall insulator with
opposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeeman
field leads to the opposite Dirac mass for adjacent edges of a square sample,
and naturally induce Majorana corner states. This topological phase can be
characterized by Majorana edge polarizations, and it is robust against
perturbations on random potentials as long as the edge gap remains open. Our
work provides a new possibility to realize a second-order topological
superfluid in two dimensions and engineer Majorana corner states.
