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Many works have shown that deep learning-based medical image classification models can exhibit bias toward certain demographic attributes like race, gender, and age. Existing bias mitigation methods primarily focus on learning debiased models, which may not necessarily guarantee all sensitive information can be removed and usually comes with considerable accuracy degradation on both privileged and unprivileged groups. To tackle this issue, we propose a method, FairPrune, that achieves fairness by pruning. Conventionally, pruning is used to reduce the model size for efficient inference. However, we show that pruning can also be a powerful tool to achieve fairness. Our observation is that during pruning, each parameter in the model has different importance for different groups' accuracy. By pruning the parameters based on this importance difference, we can reduce the accuracy difference between the privileged group and the unprivileged group to improve fairness without a large accuracy drop. To this end, we use the second derivative of the parameters of a pre-trained model to quantify the importance of each parameter with respect to the model accuracy for each group. Experiments on two skin lesion diagnosis datasets over multiple sensitive attributes demonstrate that our method can greatly improve fairness while keeping the average accuracy of both groups as high as possible.