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Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.