The precision of relative lattice parameter determinations by X-ray Bragg reflexion is usually limited to a few parts in 10$^7$ by the dispersed profiles of single spectral lines. In a new technique described herein this primary limitation is removed because changes of Bragg angle are measured in a non-dispersive double crystal arrangement. As a result it is shown that lattice parameter changes of one part in 10$^9$ can be detected. Preliminary measurements of the lattice parameter difference between a highly doped silicon sample and an undoped silicon crystal are in good agreement with measurements obtained on the same material by conventional techniques. The influence of experimental parameters on the sensitivity of the technique are considered in detail and some convenient developments of the basic method are suggested.