Feature selection is an essential preprocessing procedure in data analysis. The process refers to selecting a subset of relevant features to improve prediction performance and better understand the data. However, we notice that traditional feature selection methods have limited ability to deal with data distribution over protected features due to data imbalance and indeed protected features are selected. Two problems can occur with current feature selection methods when protected features are considered: the presence of protected features among the selected ones which often lead to unfair results and the presence of redundant features which carry potentially the same information with the protected ones. To address these issues, we introduce in this paper a fair feature selection method that takes into account the existence of protected features and their redundant. Our new method finds a set of relevant features with no protected features and with the least possible redundancy under prediction quality constraint. This constraint consists of a trade-off between fairness and prediction performance. Our experiments on well-known biased datasets from the literature demonstrated that our proposed method outperformed the traditional feature selection methods under comparison in terms of performance and fairness.