The disclosure relates to a sealed and thermally insulating tank for storing a fluid, said sealed tank comprising an outer support structure, a thermal insulating barrier retained on the support structure, and a sealing barrier supported by the thermal insulating barrier. In one embodiment, the thermal insulating barrier comprises a corner structure positioned at an intersection between a first and a second wall of the support structure, the corner structure comprising a first and a second insulating panel, each having an outer surface positioned facing the support structure, an inner surface provided with a member for securing the sealing membrane, and lateral edges, the first panel having an outer surface resting against the first wall of the support structure and a lateral edge resting against the second wall of the support structure, the second panel having an outer surface resting against the second wall of the support structure and a lateral edge resting against the outer surface of the first panel.