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Fairness has become a critical value online, and the latest studies consider it in many problems. In recommender systems, fairness is important since the visibility of items is controlled by systems. Previous fairness-aware recommender systems assume that sufficient relationship data between users and items are available. However, it is common that new users and items are frequently introduced, and they have no relationship data yet. In this paper, we study recommendation methods to enhance fairness in a cold-start state. Fairness is more significant when the preference of a user or the popularity of an item is unknown. We propose a meta-learning-based cold-start recommendation framework called FaRM to alleviate the unfairness of recommendations. The proposed framework consists of three steps. We first propose a fairness-aware meta-path generation method to eliminate bias in sensitive attributes. In addition, we construct fairness-aware user representations through the meta-path aggregation approach. Then, we propose a novel fairness objective function and introduce a joint learning method to minimize the trade-off between relevancy and fairness. In extensive experiments with various cold-start scenarios, it is shown that FaRM is significantly superior in fairness performance while preserving relevance accuracy over previous work. [ABSTRACT FROM AUTHOR]