Data replication can be used to improve the availability of data in a distributed database system. In such a system, a mechanism is required to maintain the consistency of the replicated data. Grid structure (GS) technique based on quorum is one of the latest solutions for performing this while providing a high availability of the system. It was shown in the previous study, that it still requires a bigger number of copies be made available to construct a quorum. So it is not suitable for the large systems. In this paper, we propose a technique called the binary vote assignment on grid (BVAG) technique by considering only neighbors have the replicated data. In comparison to the GS technique, BVAG requires lower communication cost for an operation, while providing higher data availability, which is preferred for large systems.