提出新方法让联邦学习模型高效删去用户数据，同时保持模型性能。

Federated Learning (FL) has received much attention in recent years. However, although clients are not required to share their data in FL, the global model itself can implicitly remember clients' local data. Therefore, it's necessary to effectively remove the target client's data from the FL global model to ease the risk of privacy leakage and implement ``the right to be forgotten". Federated Unlearning (FU) has been considered a promising way to remove data without full retraining. But the model utility easily suffers significant reduction during unlearning due to the gradient conflicts. Furthermore, when conducting the post-training to recover the model utility, the model is prone to move back and revert what has already been unlearned. To address these issues, we propose Federated Unlearning with Orthogonal Steepest Descent (FedOSD). We first design an unlearning Cross-Entropy loss to overcome the convergence issue of the gradient ascent. A steepest descent direction for unlearning is then calculated in the condition of being non-conflicting with other clients' gradients and closest to the target client's gradient. This benefits to efficiently unlearn and mitigate the model utility reduction. After unlearning, we recover the model utility by maintaining the achievement of unlearning. Finally, extensive experiments in several FL scenarios verify that FedOSD outperforms the SOTA FU algorithms in terms of unlearning and model utility.