An efficient algorithm for matching two three-dimensional point sets extracted from rigid objects is described. The algorithm begins by pairing a triplet of noncollinear points in one point set (the sensed point set) with a triplet of points in the other set (the reference point set). Then it determines the pairing for each subsequent sensed point by searching for a reference point such that the tetrahedron formed by the sensed point and the initial triplet of sensed points is congruent to that formed by the corresponding reference points. The matched points are guaranteed to be globally consistent. Thus the model test, which is computationally expensive, is not required in this algorithm. Experimental results based on simulated data are shown.