An impermeable and thermally insulated tank built into a load-bearing structure, the tank wall comprising: a thermally insulated barrier attached to a load-bearing wall and made of insulated blocks, juxtaposed in parallel rows separated from one another by gaps, an impermeable barrier supported by the thermally insulated barrier and made of welded metal sheets. Each insulated block carries, on the face of same opposite the load-bearing wall, two metal connecting strips arranged in parallel to the sides of the insulated block. The sheets of the membrane carried by the insulated block are welded to the strips. The connecting strips are rigidly connected to the insulated block carrying same. The sheets each have at least two orthogonal folds parallel to the sides of the insulated blocks, the folds being inserted into the gaps formed between two insulated blocks.