An algorithm is developed that finds the optimal orientation of a rigid molecular structure, represented by N reference sites, with respect to the same number of sites in an observed structure. The optimal orientation is found by minimizing the weighted sum of squared deviations of the rotated reference site positions from the observed site positions. The rotation is parametrized by a quaternion whose components, written as a column vector, are shown to be an eigenvector of a characteristic matrix which is defined in terms of the coordinate sets to be superimposed. The presented algorithm is particularly useful with respect to the calculation of orientational correlations of molecular structures.