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A novel set of electromagnetic boundary conditions is defined in terms of an interface of a medium belonging to the class of skewon-axion media. Such a medium class can be introduced in a simple and natural manner applying four-dimensional representation of electromagnetic media. It is shown that the novel boundary conditions generalize soft-and-hard (SH) and DB boundary conditions to SHDB conditions. As an application, reflection of a plane wave from a planar SHDB boundary is studied. It is shown that the two eigenvectors of the reflection dyadic define eigenwaves for which the SHDB boundary can be replaced by equivalent PEC or PMC boundaries. The theory is tested with numerical examples which reveal an interesting narrow-beamed reflection phenomenon associated to the SHDB boundary condition.