We use the recently developed multiple scattering theory to give a quantitative analysis of the X-ray absorption near edge structure (XANES) of haemoglobin and some of its substituents. We demonstrate that the XANES may contain information not provided by the extended X-ray absorption fine structure (EXAFS) part of the spectrum about the coordination geometry around the Fe atom, and in particular discuss the sensitivity of the XANES to the orientation of the CN group in HbCN. The anisotropy of the system leads to a strong dependence of the calculated spectrum on the polarisation of the X-rays. We show how this effect can be exploited in further XANES structural studies.