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The program USCI described in this paper makes possible the indexing of single-crystal reflexions recorded on a four-circle diffractometer. On the basis of the 2θ, ω, χ and φ values of a minimum of ten reflexions the corresponding reciprocal-lattice points in an orthogonal coordinate system can be determined. Adding and subtracting point vectors in pairs results in a multiplicity of vectors which allows the computation of all possible third-order determinants. The dominating determinants are integer multiples of the volume of the reciprocal unit cell. Vectors leading to the volume of the reciprocal cell form the basis of the indexing of the single-crystal reflexions. As an example ten reflexions of a columbite MnTa2O6 (Pbcn) and of a labradorite with a superlattice (Ca0.5Na0.5)(Si2.5Al1.5)O8 (P) are indexed.