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This paper addresses the traffic management problem for autonomous vehicles at intersections without traffic signals. In the current system, a road junction has no traffic signals when the traffic volume is low to medium. Installing infrastructure at each unsignalled crossing to coordinate autonomous cars can be formidable. We propose a novel decentralized strategy where the vehicles use a harmony matrix to find the best possible combination of the cars to cross the intersection without any crashes. We formulate a maximal clique problem using harmony matrix that maximizes the intersection throughput. This algorithm does not require communication between the vehicles. We compared our work with state-of-the-art communicative strategies and widely used traditional and modern methods for intersection management. Through extensive simulation, we showed that our algorithm is comparable to state-of-the-art and outperforms traditional methods.