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Contextual multi-armed bandit (MAB) is an important sequential decision-making problem in recommendation systems. A line of works, called the clustering of bandits (CLUB), utilize the collaborative effect over users and dramatically improve the recommendation quality. Owing to the increasing application scale and public concerns about privacy, there is a growing demand to keep user data decentralized and push bandit learning to the local server side. Existing CLUB algorithms, however, are designed under the centralized setting where data are available at a central server. We focus on studying the federated online clustering of bandit (FCLUB) problem, which aims to minimize the total regret while satisfying privacy and communication considerations. We design a new phase-based scheme for cluster detection and a novel asynchronous communication protocol for cooperative bandit learning for this problem. To protect users' privacy, previous differential privacy (DP) definitions are not very suitable, and we propose a new DP notion that acts on the user cluster level. We provide rigorous proofs to show that our algorithm simultaneously achieves (clustered) DP, sublinear communication complexity and sublinear regret. Finally, experimental evaluations show our superior performance compared with benchmark algorithms.