A method for gripping a rectangular textile item, wherein the textile item hanging from a clamp (18) that holds a corner (18) is reoriented so as to form at least part of a freely hanging periphery of the textile item that emanates from the held corner (18), wherein the textile item is reoriented from the held corner (18) thereof in the state hanging in front of a wall (29) by a holding means (37) that acquires at least one location (42, 43) of the textile item, and displacing of said holding means (37) so as to configure at least part of a periphery of the textile item hanging in front of the wall (29) that emanates from the corner (18), and gripping of a portion (46) of the periphery of the textile item hanging in front of the wall (29).