A sealed and thermally insulated tank intended for the storage of a fluid, said tank having a plurality of walls (42, 43) exhibiting a multilayer structure successively having, in the direction of the thickness from the outside to the inside of the tank, a secondary thermally insulating barrier retained against a load-bearing structure, a secondary sealing membrane borne by the secondary thermally insulating barrier, a primary thermally insulating barrier bearing against the secondary sealing membrane and a primary sealing membrane borne by the primary thermally insulating barrier and designed to be in contact with the fluid contained in the tank; a first of the walls (42, 43) having a secondary thermally insulating barrier comprising: - a first insulating panel arranged along the intersection between the load-bearing structure of said first wall and the load-bearing structure of an adjacent second wall; and - a second insulating panel juxtaposed with the first insulating panel along one edge of said first insulating panel opposing the second wall; the first and the second insulating panels (44, 50) each having an internal face opposing the load-bearing structure provided with a small metal plate (56, 82, 92, 93); the first wall having a secondary sealing membrane comprising: - a first metal sheet having at least two perpendicular corrugations (65, 66) and having a first and a second edge (61, 62) which are opposed to one another and which are parallel to the intersection between the load-bearing structure of said first wall and the load-bearing structure of an adjacent second wall, the first edge being closer to the second wall than the second edge; the first edge of the first metal sheet being, on the one hand, welded to the small metal plate of the first insulating panel to retain the first metal sheet against the first insulating panel and, on the other hand, welded to a first flange of a metal angle plate which has a second flange welded to the metal sheet of the secondary sealing membrane of the second wall; and - a second metal sheet having at least two perpendicular corrugations (90, 91), one of said corrugations being arranged in the extension of one of the corrugations of the first metal sheet, the second metal sheet having a first and a second edge (87, 88) which are opposed to one another and parallel to the intersection between the load-bearing structure of said first wall and the load-bearing structure of an adjacent second wall, the first edge being closer to the second wall than the second edge, the second edge of the first metal sheet and the first edge of the second metal sheet being welded together and in that one edge from the second edge of the first metal sheet and the first edge of the second metal sheet is a joggled edge permitting the first and the second metal sheets (60, 86) to be lap welded to one another the tank being characterized in that the second edge of the second metal sheet is welded to the small metal plate of the second insulating panel. - a first insulating panel arranged along the intersection between the load-bearing structure of said first wall and the load-bearing structure of an adjacent second wall; and - a second insulating panel juxtaposed with the first insulating panel along one edge of said first insulating panel opposing the second wall; - a first metal sheet having at least two perpendicular corrugations (65, 66) and having a first and a second edge (61, 62) which are opposed to one another and which are parallel to the intersection between the load-bearing structure of said first wall and the load-bearing structure of an adjacent second wall, the first edge being closer to the second wall than the second edge; the first edge of the first metal sheet being, on the one hand, welded to the small metal plate of the first insulating panel to retain the first metal sheet against the first insulating panel and, on the other hand, welded to a first flange of a metal angle plate which has a second flange welded to the metal sheet of the secondary sealing membrane of the second wall; and - a second metal sheet having at least two perpendicular corrugations (90, 91), one of said corrugations being arranged in the extension of one of the corrugations of the first metal sheet, the second metal sheet having a first and a second edge (87, 88) which are opposed to one another and parallel to the intersection between the load-bearing structure of said first wall and the load-bearing structure of an adjacent second wall, the first edge being closer to the second wall than the second edge,