Sealed and thermally insulating tank for storing a fluid, a tank wall having a secondary thermal insulation barrier, a secondary sealing membrane, a primary thermal insulation barrier and a primary sealing membrane supported by the primary thermal insulation barrier, where the primary insulating elements have parallelepiped insulating panels disposed so as to provide voids between them. The primary thermal insulation barrier having an anti-convective filler plate disposed in the void between a first parallelepiped insulating panel and a second parallelepiped insulating panel, the anti-convective filler plate being made of thin continuous material and having a plurality of elongated wall elements extending over substantially the entire width of the void to delimit cells extending substantially perpendicular to the thickness direction.