Abstract: A corner piece is provided for an external corner of a wall structure for use with baseboard channel members adapted to have carpet strips mounted thereon. The corner piece has an external cylindrical configuration extending between two side walls perpendicular to each other. An inner surface of the corner piece is formed by a notch defining two walls perpendicular to each other and perpendicular to the side walls, respectively. A pair of flanges are integrally molded with the corner piece and extend outwardly perpendicular to the side walls of the corner piece for engagement in complementary cut-out portions of a carpet channel member.