This paper considers the problem of group fairness in clustering. We propose a new fairness notion which strictly generalizes existing notions and we theoretically analyze the relationships between several existing notions. Finally, we propose a simple and efficient greedy round-robin-based algorithm (FRACOE) and extensive experiments to validate its efficacy across multiple datasets. © 2023 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.