Sealed and thermally insulating tank in which a first tank wall and an adjacent second tank wall form an edge, the tank further including a sealed corner piece fixed in a sealed manner to the sealing membrane of the first tank wall and of the second tank wall, the corner piece including a sheet metal corner angle-iron situated in line with the edge, a first reinforcing flange, a second reinforcing flange, a first locking piece, a second locking piece wherein the locking pieces are fixed to the insulating barrier, the first reinforcing flange and the second reinforcing flange each include a tab fixed to the lower face of the first and second locking pieces, respectively.