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Current face recognition systems achieve high progress on several benchmark tests. Despite this progress, recent works showed that these systems are strongly biased against demographic sub-groups. Consequently, an easily integrable solution is needed to reduce the discriminatory effect of these biased systems. Previous work mainly focused on learning less biased face representations, which comes at the cost of a strongly degraded overall recognition performance. In this work, we propose a novel unsupervised fair score normalization approach that is specifically designed to reduce the effect of bias in face recognition and subsequently lead to a significant overall performance boost. Our hypothesis is built on the notation of individual fairness by designing a normalization approach that leads to treating similar individuals similarly. Experiments were conducted on three publicly available datasets captured under controlled and in-the-wild circumstances. Results demonstrate that our solution reduces demographic biases, e.g. by up to 82.7% in the case when gender is considered. Moreover, it mitigates the bias more consistently than existing works. In contrast to previous works, our fair normalization approach enhances the overall performance by up to 53.2% at false match rate of 0.001 and up to 82.9% at a false match rate of 0.00001. Additionally, it is easily integrable into existing recognition systems and not limited to face biometrics.