Hemoglobin is the prototypic allosteric protein. Still, its molecular allosteric mechanism is not fully understood. To elucidate the mechanism of cooperativity on an atomistic level, we developed a novel computational technique to analyse the coupling of tertiary and quaternary motions. From Molecular Dynamics simulations showing spontaneous quaternary transitions, we separated the transition trajectories into two orthogonal sets of motions: one consisting of intra-chain motions only (referred to as tertiary-only) and one consisting of global inter-chain motions only (referred to as quaternary-only). The two underlying subspaces are orthogonal by construction and their direct sum is the space of full motions. Using Functional Mode Analysis, we were able to identify a collective coordinate within the tertiary-only subspace that is correlated to the most dominant motion within the quaternary-only motions, hence providing direct insight into the allosteric coupling mechanism between tertiary and quaternary conformation changes. This coupling-motion is substantially different from tertiary structure changes between the crystallographic structures of the T- and R-state. We found that hemoglobins allosteric mechanism of communication between subunits is equally based on hydrogen bonds and steric interactions. In addition, we were able to affect the T-to-R transition rates by choosing different histidine protonation states, thereby providing a possible atomistic explanation for the Bohr effect. 