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Learning fair representation in deep learning is essential to mitigate discriminatory outcomes and enhance trustworthiness. However previous research has been commonly established on inappropriate assumptions prone to unrealistic counterfactuals and performance degradation. Although some proposed alternative approaches such as employing correlation-aware causal graphs or proxies for mutual information these methods are less practical and not applicable in general. In this work we propose FAir DisEntanglement with Sensitive relevance (FADES) a novel approach that leverages conditional mutual information from the information theory perspective to address these challenges. We employ sensitive relevant code to direct correlated information between target labels and sensitive attributes by imposing conditional independence allowing better separation of the features of interest in the latent space. Utilizing an intuitive disentangling approach FADES consistently achieves superior performance and fairness both quantitatively and qualitatively with its straightforward structure. Specifically the proposed method outperforms existing works in downstream classification and counterfactual generations on various benchmarks.