A fast and reliable algorithm has been developed for auto-indexing oscillation images. The observed reflection positions are used to compute the corresponding reciprocal-lattice vectors assuming a stationary crystal. These vectors are then projected onto a chosen direction. The projections are subjected to a one-dimensional Fourier analysis. A large Fourier term will be found that has a periodicity corresponding to the interplanar distance if the chosen direction happens to be perpendicular to a set of widely separated reciprocal-lattice planes. Exploration of such directions over a hemisphere establishes the best potential basis vectors of the real cell. The program has successfully determined the lengths and directions of basis vectors for numerous unit cells having cell dimensions ranging from 16 to 668 Å and oscillation ranges from 0.2 to 2.0°.