Abstract: A method and apparatus is described, with which individual rectangular glass panes of thickness between 0.03 mm and 2 mm can be cut from a glass band (2) drawn vertically from a hot forming device (1) in an in-line process with reduced rejects and reduced waste. The method provides that the glass band (2) drawn vertically downward through a vertical zone is cooled below a lower cooling point of the glass and subsequently is deflected through a bending zone (3b) with a bending radius between 0.1 m and 4 m into a horizontal zone (3c) in which it is horizontally oriented. The vertical alignment of the glass band (2) in the vertical zone (3a) is continuously monitored. At least one cutting process is performed on the horizontally oriented glass band (2) in the horizontal zone (3c). The device (20) for monitoring the vertical alignment of the glass band (2) includes at least three sensors (22a, 22b, 22c; 22a′, 22b′, 22c′) that detect the glass edges These sensors can be mechanical rollers.