Sealed and thermally insulating tank comprising a sealed membrane and a thermally insulating barrier with insulating blocks comprising cover panels, the sealed membrane being made up of a corrugated metal membrane comprising a series of parallel corrugations and flat portions between the corrugations and resting on the cover panels, wherein an insulating block is twice the pitch of the corrugations, meaning that a series of corrugations comprises a pair of corrugations situated in line with one insulating block, and wherein the flat portions of the sealed membrane are arranged in line with an internal zone of the cover panels, the sealed membrane being fixed to the thermally insulating barrier by fixing the flat portions of the sealed membrane to the insulating blocks in the internal zone of the cover panels.