Method of closing a sealing membrane (24, 26) for a sealed tank, said tank being in particular thermally insulative, the method including the following steps: - furnishing a tank wall fixed to a support wall, the tank wall including in a direction of thickness a thermally-insulating barrier (23, 25) and a sealing membrane (24, 26) fixed to the thermally-insulating barrier (23, 25), the thermally-insulating barrier (23, 25) including an edge portion (232, 252) situated at one edge of the thermally-insulating barrier (23, 25) in a first direction, the method being characterised in that: - fixing a metal connecting angle-iron at the level of the edge portion (232, 252), the metal connecting angle-iron including a first flange and a second flange connected to the first flange, by welding the first flange by means of a weld bead (33, 34) to a metal part (14, 15) on the support wall, and by connecting the second flange to the sealing membrane (24, 26), in which the step of welding the first flange is carried out using an automatic welding machine moving on a welding support, the welding support including a fixing surface and a support surface perpendicular to the fixing surface, the support surface including a guide means, in particular a guide rail, extending in a second direction perpendicular to the first direction and to the direction of thickness, the welding machine including a displacement system cooperating with the guide means and configured to move the welding machine in a forward movement parallel to the second direction, the welding machine also including a welding torch, and in which during welding of the first flange the fixing surface of the welding support is fixed to the edge portion (232, 252) of the thermally-insulating barrier so that the support surface is perpendicular to the first direction. - furnishing a tank wall fixed to a support wall, the tank wall including in a direction of thickness a thermally-insulating barrier (23, 25) and a sealing membrane (24, 26) fixed to the thermally-insulating barrier (23, 25), the thermally-insulating barrier (23, 25) including an edge portion (232, 252) situated at one edge of the thermally-insulating barrier (23, 25) in a first direction, the method being characterised in that: - fixing a metal connecting angle-iron at the level of the edge portion (232, 252), the metal connecting angle-iron including a first flange and a second flange connected to the first flange, by welding the first flange by means of a weld bead (33, 34) to a metal part (14, 15) on the support wall, and by connecting the second flange to the sealing membrane (24, 26), - fixing a metal connecting angle-iron at the level of the edge portion (232, 252), the metal connecting angle-iron including a first flange and a second flange connected to the first flange, by welding the first flange by means of a weld bead (33, 34) to a metal part (14, 15) on the support wall, and by connecting the second flange to the sealing membrane (24, 26), in which the step of welding the first flange is carried out using an automatic welding machine moving on a welding support, the welding support including a fixing surface and a support surface perpendicular to the fixing surface, the support surface including a guide means, in particular a guide rail, extending in a second direction perpendicular to the first direction and to the direction of thickness, the welding machine including a displacement system cooperating with the guide means and configured to move the welding machine in a forward movement parallel to the second direction, the welding machine also including a welding torch, and in which during welding of the first flange the fixing surface of the welding support is fixed to the edge portion (232, 252) of the thermally-insulating barrier so that the support surface is perpendicular to the first direction.