Abstract: A method of and apparatus for inverting and stacking matched pairs of moving glass sheets, one on the other, having a device for longitudinally spacing the sheets of each pair relative to each other prior to their entering the inverting and stacking mechanism. A lift device, together with the inverting and stacking mechanism, holds the first sheet of the matched pair stationary above a conveyor while the second sheet is advanced therebeneath to a predetermined position at which point the first sheet is deposited on the second sheet in a closely matched relationship. Hold-down devices maintain the orientation of the first sheet relative to the second sheet.