Sealed and thermally insulating tank for storing a fluid comprising a first wall and a second wall, the first and the second wall each comprising, in a thickness direction, a bearing wall (5, 25), a thermal insulation barrier (6, 26) fixed to the bearing wall (5, 25), a sealing membrane (7, 27) parallel to the bearing wall (5, 25) and fixed to the thermal insulation barrier (6, 26), the sealed and thermally insulating tank comprising, at an edge corner (100, 201) between the bearing wall of the first wall and the bearing wall of the second wall, a corner structure, the corner structure comprising: - a first anchoring flange fixed to the bearing wall of the second wall, - a second anchoring flange fixed to the bearing wall of the first wall, - a sealing corner piece fixed, on the one hand, to the first anchoring flange via a first connecting piece and, on the other hand, to the second anchoring flange via a second connecting piece, the sealing corner piece being connected in a sealed manner to the sealing membrane of the first wall and to the sealing membrane of the second wall, the sealing corner piece comprising a first flat branch extending in the plane of the sealing membrane of the second wall, and a second flat branch extending in the plane of the sealing membrane of the first wall, the first connecting piece comprising a first flat branch parallel to the first anchoring flange, the second connecting piece comprising a first flat branch parallel to the second anchoring flange, the first flat branch of the first connecting piece being welded to the first anchoring flange, the first flat branch of the second connecting piece being welded to the second anchoring flange, characterised in that the first connecting piece comprise a second flat branch parallel to the sealing membrane of the second wall, and the second connecting piece comprise a second flat branch parallel to the sealing membrane of the first wall, the first flat branch of the sealing corner piece being welded to the second flat branch of the first connecting piece, and the second flat branch of the sealing corner piece being welded to the second flat branch of the second connecting piece, the sealing membrane of the first wall being welded to the second flat flat branch of the sealing corner piece, and the sealing membrane of the second wall being welded to the first flat branch of the sealing corner piece. - a first anchoring flange fixed to the bearing wall of the second wall, - a second anchoring flange fixed to the bearing wall of the first wall, - a sealing corner piece fixed, on the one hand, to the first anchoring flange via a first connecting piece and, on the other hand, to the second anchoring flange via a second connecting piece, the sealing corner piece being connected in a sealed manner to the sealing membrane of the first wall and to the sealing membrane of the second wall, the sealing corner piece comprising a first flat branch extending in the plane of the sealing membrane of the second wall, and a second flat branch extending in the plane of the sealing membrane of the first wall, the first connecting piece comprising a first flat branch parallel to the first anchoring flange, the second connecting piece comprising a first flat branch parallel to the second anchoring flange, the first flat branch of the first connecting piece being welded to the first anchoring flange, the first flat branch of the second connecting piece being welded to the second anchoring flange, characterised in that the first connecting piece comprise a second flat branch parallel to the sealing membrane of the second wall, and the second connecting piece comprise a second flat branch parallel to the sealing membrane of the first wall, the first flat branch of the sealing corner piece being welded to the second flat branch of the first connecting piece, and the second flat branch of the sealing corner piece being welded to the second flat branch of the second connecting piece, the sealing membrane of the first wall being welded to the second flat flat branch of the sealing corner piece, and the sealing membrane of the second wall being welded to the first flat branch of the sealing corner piece.