Radiation damage in macromolecular crystals is not suppressed even at 90 K. This is particularly true for covalent bonds involving an anomalous scatterer (such as bromine) at the `peak wavelength'. It is shown that a series of absorption spectra recorded on a brominated RNA faithfully monitor the extent of cleavage. The continuous spectral changes during irradiation preserve an `isosbestic point', each spectrum being a linear combination of `zero' and `infinite' dose spectra. This easily yields a good estimate of the partial occupancy of bromine at any intermediate dose. The considerable effect on the near-edge features in the spectra of the crystal orientation versus the beam polarization has also been examined and found to be in good agreement with a previous study. Any significant influence of the (C-Br bond/beam polarization) angle on the cleavage kinetics of bromine was also searched for, but was not detected. These results will be useful for standard SAD/MAD experiments and for the emerging `radiation-damage-induced phasing' method exploiting both the anomalous signal of an anomalous scatterer and the `isomorphous' signal resulting from its cleavage.