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Despite the remarkable success achieved by graph convolutional networks for functional brain activity analysis, the heterogeneity of functional patterns and the scarcity of imaging data still pose challenges in many tasks. Transferring knowledge from a source domain with abundant training data to a target domain is effective for improving representation learning on scarce training data. However, traditional transfer learning methods often fail to generalize the pre-trained knowledge to the target task due to domain discrepancy. Self-supervised learning on graphs can increase the generalizability of graph features since self-supervision concentrates on inherent graph properties that are not limited to a particular supervised task. We propose a novel knowledge transfer strategy by integrating meta-learning with self-supervised learning to deal with the heterogeneity and scarcity of fMRI data. Specifically, we perform a self-supervised task on the source domain and apply meta-learning, which strongly improves the generalizability of the model using the bi-level optimization, to transfer the self-supervised knowledge to the target domain. Through experiments on a neurological disorder classification task, we demonstrate that the proposed strategy significantly improves target task performance by increasing the generalizability and transferability of graph-based knowledge.