Smart contracts have enabled blockchain systems to evolve from simple cryptocurrency platforms, such as Bitcoin, to general transactional systems, such as Ethereum. Catering for emerging business requirements, a new architecture called execute-order-validate has been proposed in Hyperledger Fabric to support parallel transactions and improve the blockchain's throughput. However, this new architecture might render many invalid transactions when serializing them. This problem is further exaggerated as the block formation rate is inherently limited due to other factors beside data processing, such as cryptography and consensus. In this work, we propose a novel method to enhance the execute-order-validate architecture, by reducing invalid transactions to improve the throughput of blockchains. Our method is inspired by state-of-the-art optimistic concurrency control techniques in modern database systems. In contrast to existing blockchains that adopt database's preventive approaches which might abort serializable transactions, our method is theoretically more fine-grained. Specifically, unserializable transactions are aborted before ordering and the remaining transactions are guaranteed to be serializable. For evaluation, we implement our method in two blockchains respectively, FabricSharp on top of Hyperledger Fabric, and FastFabricSharp on top of FastFabric. We compare the performance of FabricSharp with vanilla Fabric and three related systems, two of which are respectively implemented with one standard and one state-of-the-art concurrency control techniques from databases. The results demonstrate that FabricSharp achieves 25% higher throughput compared to the other systems in nearly all experimental scenarios. Moreover, the FastFabricSharp's improvement over FastFabric is up to 66%.