The evolution of the band texture, that develops in a lyotropic chiral nematic (cholesteric) PBDG solution after cessation of flow, is determined by means of a polarizing microscope equipped with a shear-flow cell. Both the red and the conoscopic SALS images are used to obtain information on the increase of the band spacing as a function of relaxation time. Also, a relation between the previously applied shear rate and the lateral band size is observed. The experimental results on the band spacing are compared to a simple one-dimensional (1-D) continuum mechanical model that uses the bend Frank elastic constant and the Miesowicz rotational viscosity. The difference between the time dependence of the lateral and the longitudinal relaxation is discussed in terms of the difference between the splay and the bend elastic constant. The spontaneous formation of a band texture during relaxation is demonstrated using a 2-D lattice model. The average "domain size" during flow as a function of shear rate is predicted using some simple arguments. This prediction is compared to the experimental results.