Hofmeister effects continue to defy all-encompassing theories, and their origin is still a matter of debate. We observed strong Hofmeister effects in Ca2+/Na+ exchange on a permanently charged surface over a wide range of ionic strengths. They could not be attributed to dispersion forces, classical induction forces, ionic size, or hydration effects. We demonstrated that another stronger force was active in the ion-surface interactions, and which would create Hofmeister effects in general. The strength of this force was up to 10(4) times that of the classical induction force, and could be comparable to the Coulomb force. Coulomb, dispersion and hydration effects appeared to be interwined to affect the force. The presence of the observed strong non-classical induction force implied that energies of non-valence electrons of ions/atoms at the interface might be heavily underestimated in current theories, and possibly just those underestimated energies of non-valence electrons determined Hofmeister effects.