The generalization capacity of Multi-Task Learning (MTL) becomes limited when unrelated tasks negatively impact each other by updating shared parameters with conflicting gradients, resulting in negative transfer and a reduction in MTL accuracy compared to single-task learning (STL). Recently, there has been an increasing focus on the fairness of MTL models, necessitating the optimization of both accuracy and fairness for individual tasks. Similarly to how negative transfer affects accuracy, task-specific fairness considerations can adversely influence the fairness of other tasks when there is a conflict of fairness loss gradients among jointly learned tasks, termed bias transfer. To address both negative and bias transfer in MTL, we introduce a novel method called FairBranch. FairBranch branches the MTL model by assessing the similarity of learned parameters, grouping related tasks to mitigate negative transfer. Additionally, it incorporates fairness loss gradient conflict correction between adjoining task-group branches to address bias transfer within these task groups. Our experiments in tabular and visual MTL problems demonstrate that FairBranch surpasses state-of-the-art MTL methods in terms of both fairness and accuracy.