Cyberbullying is a widespread adverse phenomenon among online social interactions in today's digital society. While numerous computational studies focus on enhancing the cyberbullying detection performance of machine learning algorithms, proposed models tend to carry and reinforce unintended social biases. In this study, we try to answer the research question of "Can we mitigate the unintended bias of cyberbullying detection models by guiding the model training with fairness constraints?". For this purpose, we propose a model training scheme that can employ fairness constraints and validate our approach with different datasets. We demonstrate that various types of unintended biases can be successfully mitigated without impairing the model quality. We believe our work contributes to the pursuit of unbiased, transparent, and ethical machine learning solutions for cyber-social health.