The invention relates to a sealed and thermally insulated tank for storing a fluid comprising a thermal insulation barrier and a sealing membrane supported by the thermal insulation barrier, the thermal insulation barrier comprising a plurality of juxtaposed parallelepidal insulating blocks (3, 7) each one comprising: - a bottom panel (10) and a cover panel (11), which are spaced apart in a thickness direction of the insulating block (3, 7); - a plurality of pillars (13) interposed between said bottom (10) and cover (11) panels and extending in a thickness direction; and - a lagging lining placed between the pillars (13); said plurality of insulating blocks (3, 7) comprising at least one reinforced insulating block (3, 7) equipped with at least one anti-overspill reinforcing structure (14) extending longitudinally along a reinforced lateral face of said reinforced insulating block (3, 7), between the bottom panel (10) and the cover panel (11).