The order of electron pairs with anti-parallel (Coulomb) and parallel (Fermi) spins, existing in a molecule, is quantified and compared. Information entropies, providing a measure of the (dis)order of Coulomb and Fermi pairs, are defined. The corresponding probabilities are calculated in orbital spaces appropriate for population analysis, as the natural atomic orbitals. The pi-bonding of butadiene molecule is considered as a model system, and the (dis)order of electron pairs is examined in both Hartree-Fock and CI levels. It turns out that chemical bonding imposes an increase of the order of both Coulomb and Fermi pairs; however, Fermi pairs are more ordered, that is involve more structure than the Coulomb ones; this holds remarkably in all approximation levels. (C) 2004 Elsevier B.V. All rights reserved.