From an experimental study on the linkage between dimer-tetramer association and oxygen binding in human hemoglobin it is found that triliganded tetramers α2β2(O2)3 have an affinity for oxygen that is significantly higher than that of α1β1 dimers (superscripts denote intersubunit contacts). This conclusion is based upon a newly determined series of accurate oxygen binding isotherms, which were analyzed in conjunction with independently determined values of the dimer-tetramer equilibrium constants in the unliganded and fully oxygenated states [Ip, S. H. C. & Ackers, G. K. (1977) J. Biol. Chem. 252, 82-87]. The results imply that in the molecule α2β2(O2)3 the interactions at the α1β2 intersubunit contacts are propagated to the unliganded heme in a manner that increases its affinity for oxygen. This effect contrasts sharply with the well-known reduction in oxygen affinity arising from these same contacts when unliganded dimers are assembled to form unliganded α2β2 tetramers. The magnitude of the enhancement in affinity at the unliganded site in triliganded tetramers (0.81 kcal, 3.39 kJ) is approximately one-fourth as great as the reduction in affinity on each heme site that arises from subunit assembly of the unliganded tetramer. The terms “quaternary constraint” and “quaternary enhancement” are employed to describe these oppositely directed effects of intersubunit interaction upon heme-site affinity. Experimental results also suggest that dimers bind oxygen with a higher affinity than monomeric α and β chains do under the same temperature and buffer conditions (21.5°C, pH 7.40, 0.1 M Tris·Hcl/0.1 M NaCl/1 mM Na2EDTA). Thus quaternary enhancement may be manifested at the α1β1 contacts. Implications of these results for models of the cooperative mechanism are discussed.