We present a nuclear magnetic resonance (NMR) study in solution of the structures of human normal hemoglobin (Hb A) in the deoxy or unligated form in the absence and presence of an allosteric effector, inositol hexaphosphate (IHP), using 15N-1H residual dipolar coupling (RDC) measurements. There are several published crystal structures for deoxyhemoglobin A (deoxy-Hb A), and it has been reported that the functional properties of Hb A in single crystals are different from those in solution. Carbonmonoxyhemoglobin A (HbCO A) can also be crystallized in several structures. Our recent RDC studies of HbCO A in the absence and presence of IHP have shown that the solution structure of this Hb molecule is distinctly different from its classical crystal structures (R and R2). To have a better understanding of the structure-function relationship of Hb A under physiological conditions, we need to evaluate its structures in both ligated and unligated states in solution. Here, the intrinsic paramagnetic property of deoxy-Hb A has been exploited for the measurement of RDCs using the magnetic-field dependence of the apparent one-bond 1H-15N J couplings. Our RDC analysis suggests that the quaternary and tertiary structures of deoxy-Hb A in solution differ from its recently determined high-resolution crystal structures. Upon binding of IHP, structural changes in deoxy-Hb A are also observed, and these changes are largely within the alpha1beta1 (or alpha2beta2) dimer itself. These new structural findings allow us to gain a deeper insight into the structure-function relationship of this interesting allosteric protein.