It frequently occurs that a biological assembly in a crystallographic asymmetric unit has more than one noncrystallographic symmetry operator. For instance, a tetramer might have the point group 222 or a spherical virus will have the point group 532. A self-rotation function searches for the direction and angle of rotation of the individual noncrystallographic symmetry operations, while a cross-rotation function searches for the relationship of a structure in one unit cell with similar structures in another cell. The power of the rotation function can be greatly enhanced by searching for all noncrystallographic symmetry operators simultaneously. The procedure described previously [Rossmann, Ford, Watson & Banaszak (1972). J. Mol. Biol. 64, 237-249] has been generalized. The increased power of this 'locked' rotation function permits a good determination of the orientation of an icosahedral virus in the presence of less than 1% of the possible diffraction data to 7 A resolution. In addition, the peak-to-noise ratio is substantially improved.