A new formulation of nonmetric multidimensional scaling using the STRAIN criterion is proposed. Innovative features of the new formulation include: the parameterization of the p-dimensional distance matrices by the positive semidefinite matrices of rank >=p; optimization of the disparity variables, rather than the configuration coordinate variables; and a new nondegeneracy constraint, which restricts the set of disparities rather than the set of distances. It is demonstrated that this formulation allows the identification of globally optimal configurations. The method is applied to two famous data sets.