Method of closing a sealing membrane 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 and a sealing membrane fixed to the thermally-insulating barrier , the thermally-insulating barrier including an edge portion situated at one edge of the thermally-insulating barrier in a first direction, the method being characterised in that : - fixing a metal connecting angle-iron at the level of the edge portion , 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 to a metal part on the support wall, and by connecting the second flange to the sealing membrane , 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 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 and a sealing membrane fixed to the thermally-insulating barrier , the thermally-insulating barrier including an edge portion situated at one edge of the thermally-insulating barrier in a first direction, the method being characterised in that : - fixing a metal connecting angle-iron at the level of the edge portion , 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 to a metal part on the support wall, and by connecting the second flange to the sealing membrane , - fixing a metal connecting angle-iron at the level of the edge portion , 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 to a metal part on the support wall, and by connecting the second flange to the sealing membrane , 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 of the thermally-insulating barrier so that the support surface is perpendicular to the first direction. <EOS>