Accurate measurements of the lattice constant of cadmium mercury telluride (CdxHg1-x,Te, or CMT) grown by molecular beam epitaxy (MBE) are reported For the composition range 0 less than or equal tox<0.5. The lattice constants of substrate and layer are measured simultaneously by high-resolution X-ray diffraction using Bond's method. The unstrained (fully relaxed) CMT lattice constant is obtained by correcting for misfit strain distortion, based on literature values for elastic constants, The validity of this correction is verified by measurements at varying amounts of elastic deformation, by exploiting substrate inhomogeneity. Due to the low growth temperature, it is argued that the CMT lattice constants obtained correspond to those of nearly stoichiometric material. No significant lattice constant differences are observed in samples from an independent laboratory, The results show that CMT obeys Vegard's law to within the measurement uncertainty. The observed composition dependence of the CMT lattice constant corresponds to lattice constants of 6.46152 for HgTe and 6.4815 Angstrom for CdTe at 25 degreesC. A discussion of measurement uncertainties is given.