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A novel set of SHDB boundary conditions, generalizing those of the soft-and-hard boundary and the DB boundary, was recently introduced in terms of an interface of a medium belonging to the class of skewon-axion media. In this letter, the same boundary conditions are shown to arise at the interface of certain bi-anisotropic pseudochiral media. Realization of such a medium in terms of helical and metamaterial inclusions or omega-shaped particles is suggested. Plane-wave propagation in the pseudochiral medium is analyzed in terms of wavefield expansions.