The dependence of the superconducting transition temperature Tc on the excess oxygen content δ has been investigated for Bi2>Sr2>CaCu2>O8+δ annealed under high pressures of oxygen. With increasing δ, Tc decreases for δ≲0.3 and then becomes constant for δ≳0.3. It has been found by chemical titration that this strange δ dependence of Tc is related to the δ dependence of the average valency of Cu ions. That is, the average valency increases with increasing δ for δ≲0.3 and then is saturated for δ≳0.3. For δ≳0.3, the Curie-Weiss component in the DC magnetic susceptability has been found to increase with increasing δ. Therefore, the saturation is ascribed to the fact that most of the excess oxygen atoms exceeding δ≈0.3 are introduced in the form of O2 instead of O2-.