Following on from the earlier work of Pulay and Fogarasi [J. Chem. Phys. 96, 2856 (1992)] we present an alternative definition of natural internal coordinates. This set of delocalized internal coordinates can be generated for any molecular topology, no matter how complicated, and is fully nonredundant. Using an appropriate Schmidt-orthogonalization procedure, all standard bond length, bond angle, and dihedral angle constraints can be imposed within our internal coordinate scheme. Combinatorial constraints (in which sums or differences of stretches, bends, and torsions remain constant) can also be imposed. Optimizations on some fairly large systems (50-100 atoms) show that delocalized internal coordinates are far superior to Cartesians even with reliable Hessian information available at the starting geometry.