With a and b as overlapping atomic orbitals to form the A–B bonding molecular orbital ψ_ab = a + kb, it is deduced that for k ≠ 0, 1, or ∞, either the A atom or the B atom in the one-electron bond valence bond structure (A · B) exhibits increased-valence or electronic hypervalence, namely its valence exceeds unity. The result is illustrated using the results of STO-6G valence bond calculations for the one-electron bond of LiH⁺ and an excited state for H₂CN. Valencies for the ground-states of H₂⁺, H₂, and H₂^- are also considered.