The invention concerns a corner piece intended for the construction of a sealing membrane of a fluid storage tank. The corner piece (1) comprises first and second wings (2, 3) inclined relative to each other and joining at an edge, said corner piece (1) comprising an undulation (8) extending longitudinally from one end to the other of the corner piece (1) in such a way as to allow the corner piece to be deformed in a transverse direction, parallel to the edge (4); the undulation (8) comprising a first end portion (8a), a second end portion (8b) and a central portion (8c) extending between the first and second end portions (8b, 8c), in the extension of same; the first and second end portions (8a, 8c) of the undulation (8) projecting towards the outside of the corner piece (1) and the central portion (8a) projecting towards the inside of the corner piece (1).