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In recommender systems, one common challenge is the cold-start problem, where interactions are very limited for fresh users in the systems. To address this challenge, recently, many works introduce the meta-optimization idea into the recommendation scenarios, i.e. learning to learn the user preference by only a few past interaction items. The core idea is to learn global shared meta-initialization parameters for all users and rapidly adapt them into local parameters for each user respectively. They aim at deriving general knowledge across preference learning of various users, so as to rapidly adapt to the future new user with the learned prior and a small amount of training data. However, previous works have shown that recommender systems are generally vulnerable to bias and unfairness. Despite the success of meta-learning at improving the recommendation performance with cold-start, the fairness issues are largely overlooked. In this paper, we propose a comprehensive fair meta-learning framework, named CLOVER, for ensuring the fairness of meta-learned recommendation models. We systematically study three kinds of fairness - individual fairness, counterfactual fairness, and group fairness in the recommender systems, and propose to satisfy all three kinds via a multi-task adversarial learning scheme. Our framework offers a generic training paradigm that is applicable to different meta-learned recommender systems. We demonstrate the effectiveness of CLOVER on the representative meta-learned user preference estimator on three real-world data sets. Empirical results show that CLOVER achieves comprehensive fairness without deteriorating the overall cold-start recommendation performance.