The determination of accurate elevation data using laser altimetry relies on accurate knowledge of the instrument pointing angle. The Geoscience Laser Altimeter System (GLAS) on the Ice, Cloud and land Elevation Satellite (ICESat) uses a novel system for determination of the laser pointing vector. In this paper we describe this system, as well as the method used to process its data, which are required to meet ICESat's science objectives. We discuss the necessary modifications to processing techniques, implemented to optimize accuracy for the various operating conditions. Results to date are compared to calibration/validation data to assess their accuracy. We show that the stated requirements have been met for near nominal operating conditions.