does O2 binding hemoglobin always increase hemoglobin's O2 affinity?

[tdod]

I know that when oxygen binds the first hemoglobin subunit, the remaining subunits experience an increased O2 affinity. However, the hemoglobin O2 dissociation curve is sigmoidal... so, does that mean that when the third subunit is bound by O2, the fourth subunit experiences an decreased, rather than an increased O2 affinity?

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[Cawolf]

The cooperativity of the hemoglobin subunits results in increased affinity with the saturation of each site - so the answer to your question is no.

The sigmoidal shape does show that there is a limit with diminishing returns at high PO2, but the curve is always positive, so at no point does it reflect a decrease in affinity.