The urging societal demand for fair AI systems has put pressure on the research community to develop predictive models that are not only globally accurate but also meet new fairness criteria, reflecting the lack of disparate mistreatment with respect to sensitive attributes (e.g. gender, ethnicity, age). In particular, the variability of the errors made by certain Facial Recognition (FR) systems across specific segments of the population compromises the deployment of the latter, and was judged unacceptable by regulatory authorities. Designing fair FR systems is a very challenging problem, mainly due to the complex and functional nature of the performance measure used in this domain (i.e. ROC curves) and because of the huge heterogeneity of the face image datasets usually available for training. In this paper, we propose a novel post-processing approach to improve the fairness of pre-trained FR models by optimizing a regression loss which acts on centroid-based scores. Beyond the computational advantages of the method, we present numerical experiments providing strong empirical evidence of the gain in fairness and of the ability to preserve global accuracy.