The oxyhaemoglobin dissociation curve can move!

 

The oxyhaemoglobin dissociation curve shows the relationship between oxygen saturation of haemoglobin and the PO₂. Normal is shown in blue.

This relationship changes with several factors, as shown in the picture. A right shift means the haemoglobin holds the oxygen less tightly, and left shift means it will hold oxygen more tightly.

A practical physiological result of this is that in an exercising muscle (so raised temperature, lots of CO₂, and a lower pH), haemoglobin will hold less tightly to oxygen - it will let it go exactly where it's needed.

When the haemoglobin gets back to the lungs (where CO₂ drops because it's being exhaled, and so pH rises, and temperature drops a bit), then haemoglobin binds oxygen more tightly and efficiently takes it up - ready to deliver in the muscle.