Electronic and magnetic properties of small Co-O atomic clusters (“quantum wires”) have been studied in the framework of the Hartree-Fock (HF) method. The obtained results indicate that non-stoichiometric Co - O molecules with more than two O atoms possess at least one remarkably stretchable O-O bond that may facilitate significant re-construction of such molecules to larger structures. This re-construction may result in energetically favorable spin re-alignment in “antiferromagnetic” HF singlet Co-O molecules converting the singlets to larger “ferromagnetic” HF triplets and pentets. Such a spin re-alignment is energetically favorable, and may happen at the antiferromagnet-ferromagnet interface in “critical” core (Co) – shell (CoO) exchange-biased nanoclusters, providing for minimization of the surface energy, and leading to a loss of exchange bias. The obtained results are in agreement with available experimental and computational data.