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In this work, we focus on the challenging task, neuro-disease classification, using functional magnetic resonance imaging (fMRI). In population graph-based disease analysis, graph convolutional neural networks (GCNs) have achieved remarkable success. However, these achievements are inseparable from abundant labeled data and sensitive to spurious signals. To improve fMRI representation learning and classification under a label-efficient setting, we propose a novel and theory-driven self-supervised learning (SSL) framework on GCNs, namely Graph CCA for Temporal self-supervised learning on fMRI analysis GATE. Concretely, it is demanding to design a suitable and effective SSL strategy to extract formation and robust features for fMRI. To this end, we investigate several new graph augmentation strategies from fMRI dynamic functional connectives (FC) for SSL training. Further, we leverage canonical-correlation analysis (CCA) on different temporal embeddings and present the theoretical implications. Consequently, this yields a novel two-step GCN learning procedure comprised of (i) SSL on an unlabeled fMRI population graph and (ii) fine-tuning on a small labeled fMRI dataset for a classification task. Our method is tested on two independent fMRI datasets, demonstrating superior performance on autism and dementia diagnosis.