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Group Fairness-aware Continual Learning (GFCL) aims to eradicate discriminatory predictions against certain demographic groups in a sequence of diverse learning tasks.This paper explores an even more challenging GFCL problem – how to sustain a fair classifier across a sequence of tasks with covariate shifts and unlabeled data. We propose the MacFRL solution, with its key idea to optimizethe sequence of learning tasks. We hypothesize that high-confident learning can be enabled in the optimized task sequence, where the classifier learns from a set of prioritized tasks to glean knowledge, thereby becoming more capable to handle the tasks with substantial distribution shifts that were originally deferred. Theoretical and empirical studies substantiate that MacFRL excels among its GFCL competitors in terms of prediction accuracy and group fair-ness metrics.