Hyperspectral imaging (HSI) is a remote sensing technique that has been successfully applied for the task of damage detection in glass fibre-reinforced plastic (GFRP) materials. Similarly to other vision-based detection methods, one of the drawbacks of HSI is its susceptibility to the lighting conditions during the imaging, which is a serious issue for gathering hyperspectral data in real-life scenarios. In this study, a data conditioning procedure is proposed for improving the results of damage detection with various classifiers. The developed procedure is based on the concept of signal stationarity and cointegration analysis, and achieves its goal by performing the detection and removal of the non-stationary trends in hyperspectral images caused by imperfect lighting. To evaluate the effectiveness of the proposed method, two damage detection tests have been performed on a damaged GFRP specimen: one using the proposed method, and one using an established damage detection workflow, based on the works of other authors. Application of the proposed procedure in the processing of a hyperspectral image of a damaged GFRP specimen resulted in significantly improved accuracy, sensitivity, and F-score, independently of the type of classifier used.