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In recent years, three new absorbing boundary conditions (ABCs) have appeared in the literature, namely, the multiple absorbing surfaces, the reradiating boundary condition, and the Huygens ABC (HABC). The last is a generalization of the first two. The HABC mainly relies on the radiation of a field opposite to the outgoing field by means of surface currents. This paper focuses on the implementation of the HABC in the corner regions of computational domains. It is shown rigorously that the Huygens surface radiating the opposite field is not a normal Shelkunoff surface. Additional branches, called extensions, must be added in the corner regions.