The contribution of the α1β1half‐oxygenated tetramer [αβ:αO2βO2] (species 21) to human hemoglobin cooperativity was evaluated using cryogenic isoelectric focusing. The cooperative free energy of binding, reflecting O2‐driven protein structure changes, was measured as 21ΔGc = 5.1 ± 0.3 kcal for the Zn/FeO2 analog. For the Fe/FeCN analog, 21ΔGc was estimated as 4.0 kcal after correction for a CN ligand rearrangement artifact, demonstrating that ligand rearrangement does not invalidate previous conclusions regarding this species. In the context of the entire Hb cooperativity cascade, which includes eight intermediate species, the 21 tetramer is highly abundant relative to the other doubly‐ligated species, providing strong support for the previously determined consensus partition function of O2 binding and for the Symmetry Rule model of hemoglobin cooperativity (Ackers et al., Science 1992;255:54–63). Cooperativity of normal human hemoglobin is shown to depend on site‐configuration, and not solely the number of O2 bound, nor the occupancy of α vs. β subunits. Verification of a unique contribution from the α1β1doubly‐oxygenated species to the equilibrium O2 binding curve strongly reinforces the Symmetry Rule interpretation that the α1β1dimer acts both as a structural and functional element in cooperative O2 binding. Proteins 2000;41:23–43. © 2000 Wiley‐Liss, Inc.