The invention relates to a sealed and thermally insulating tank integrated into a supporting structure jointly forming an edge, the tank comprising two tank walls supported, the supporting structure connected by a corner structure at the edge, each wall of tank comprising a secondary thermally insulating barrier, a secondary waterproof membrane, a primary thermally insulating barrier and a primary waterproof membrane, the primary insulating barrier comprising a corner insulating block (30) comprising a first lateral element and a second lateral element connected by a spacer element, each side element having a bottom face resting on the secondary waterproof membrane of a respective tank wall, the corner insulating block (30) further comprising a rear face connecting the two bottom faces of so as to provide a space (43) between said rear face of the corner insulating block (30) and the secondary waterproof membrane.
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