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Existing permissioned blockchains often rely on coordination-based consensus protocols to ensure the safe execution of applications in a Byzantine environment. Furthermore, these protocols serialize the transactions by ordering them into a total global order. The serializability preserves the correctness of the application's state stored on the blockchain. However, using coordination-based protocols to attain the global order of transactions can limit the throughput and induce high latency. In contrast, application-level correctness requirements exist that are not dependent on the order of transactions, known as invariant-confluence (I-confluence). The I-confluent applications can execute in a coordination-free manner benefiting from the improved performance compared to the coordination-based approaches. The safety and liveness of I-confluent applications are studied in non-Byzantine environments, but the correct execution of such applications remains a challenge in Byzantine coordination-free environments. This work introduces OrderlessChain, a coordination-free permissioned blockchain for the safe and live execution of I-confluent applications in a Byzantine environment. We implemented a prototype of our system, and our evaluation results demonstrate that our coordination-free approach performs better than coordination-based blockchains.