A Sealed and thermally insulated tank has a tank wall on a carrier structure. The tank wall has an insulating barrier, sealed barrier and an anchoring member. The sealed barrier has a first undulating metal membrane and a second undulating metal membrane which are located at one side and the other of the anchoring member, along an assembly edge which is oriented parallel with a longitudinal direction of the anchoring member. The first and the second membrane undulate with a first series of undulations which intersect with the assembly edge Terminal undulation portions which are associated with the first series of undulations of the first membrane extend in a direction transverse to the assembly edge in the direction of the second membrane, beyond the terminal undulation portions which are associated with the first series of undulations of the second membrane.