An edge clamping device comprising: a two-position holding device having a pair of holding chucks (71, 72) that hold two separate portions of a rectangular piece of cloth that are on or near a ridge of a fold, in a state where the cloth has been folded with a side edge on a side to be located (Yc) and the opposite side edge (Yd) intersecting each other so as to reveal a right-angled triangular part of which an adjacent side (Sa) is formed by a portion of the side edge on the side to be located (Yc) that is adjacent to a corner of intersection while a hypotenuse (Sb) is formed by a portion of the opposite side edge (Yd) that defines the corner of intersection with the adjacent side (Sa); an edge locating conveyor that is disposed under the two-position holding device with a delivery direction oriented in a direction orthogonal to a direction in which the pair of holding chucks (71, 72) face each other, and delivers the cloth having been released from the two-position holding device; and a clamping chuck (92, 93) disposed downstream of the edge locating conveyor in the delivery direction, the two-position holding device releasing the two held portions separately and letting them fall onto the edge locating conveyor at different timings such that the portion on the side of the right-angled triangular part follows; the adjacent side (Sa) of the right-angled triangular part being located on the edge locating conveyor; the clamping chuck (92, 93) clamping a peripheral portion inside the right-angled triangular part including the located adjacent side (Sa), and a sensor that detects a position of a right-angled portion (Sc) of the right-angled triangular part in a state where the two-position holding device is holding two portions of the cloth, characterized in that the edge clamping device includes a position changing means that moves at least one of the two-position holding device, the edge locating conveyor, and the clamping chuck (92, 93) in a crosswise direction relative to the delivery direction such that the right-angled triangular part of the cloth held by the two-position holding device is located at a correct clamping position corresponding to the position of the clamping chuck (92, 93), and the position changing means is configured to move at least one of the two-position holding device, the edge locating conveyor, and the clamping chuck (92, 93) in a crosswise direction relative to the delivery direction based on the position of the right-angled portion (Sc) detected by the sensor. a two-position holding device having a pair of holding chucks (71, 72) that hold two separate portions of a rectangular piece of cloth that are on or near a ridge of a fold, in a state where the cloth has been folded with a side edge on a side to be located (Yc) and the opposite side edge (Yd) intersecting each other so as to reveal a right-angled triangular part of which an adjacent side (Sa) is formed by a portion of the side edge on the side to be located (Yc) that is adjacent to a corner of intersection while a hypotenuse (Sb) is formed by a portion of the opposite side edge (Yd) that defines the corner of intersection with the adjacent side (Sa); an edge locating conveyor that is disposed under the two-position holding device with a delivery direction oriented in a direction orthogonal to a direction in which the pair of holding chucks (71, 72) face each other, and delivers the cloth having been released from the two-position holding device; and a clamping chuck (92, 93) disposed downstream of the edge locating conveyor in the delivery direction, the two-position holding device releasing the two held portions separately and letting them fall onto the edge locating conveyor at different timings such that the portion on the side of the right-angled triangular part follows; the adjacent side (Sa) of the right-angled triangular part being located on the edge locating conveyor; the clamping chuck (92, 93) clamping a peripheral portion inside the right-angled triangular part including the located adjacent side (Sa), and a sensor that detects a position of a right-angled portion (Sc) of the right-angled triangular part in a state where the two-position holding device is holding two portions of the cloth, characterized in that the edge clamping device includes a position changing means that moves at least one of the two-position holding device, the edge locating conveyor, and the clamping chuck (92, 93) in a crosswise direction relative to the delivery direction such that the right-angled triangular part of the cloth held by the two-position holding device is located at a correct clamping position corresponding to the position of the clamping chuck (92, 93), and the position changing means is configured to move at least one of the two-position holding device, the edge locating conveyor, and the clamping chuck (92, 93) in a crosswise direction relative to the delivery direction based on the position of the right-angled portion (Sc) detected by the sensor.