Our knowledge of the structure of condensed matter has been based primarily on spectroscopic methods that measure first-order pair correlations of atomic arrangements and thus provide interatomic distances (for example neutron and X-ray scattering). Bond angles are given by higher-order correlation functions, and such information can be provided by X-ray absorption near-edge structure (XANES) spectroscopy, the features of which are determined by multiple scattering of photoelectrons whose paths begin and end at the selected absorbing atom. We report here angular-resolved XANES spectroscopy of a single crystal of carboxymyoglobin (MbCO). The large dichroism of the X-ray absorption of the crystal can be fully interpreted by multiple-scattering theory which allows the determination of Fe-ligand bond angles. The analysis of the identified multiple scattering features due to CO in high signal-to-noise-ratio spectra of protein in solution has allowed the determination of the variation of CO bond angles. This opens the way to the determination of subtle structural features due to bond angle variations in proteins in solution which are relevant to an understanding of the characteristics of proteins at the atomic scale.