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Data Mining is a Technology to explore data, analyze the data and finally discovering patterns from large data repository. In this paper, the problem of online mining of association rules in large databases is discussed. Online association rule mining can be applied which helps to remove redundant rules and helps in compact representation of rules for user. In this paper, a new and more optimized algorithm has been proposed for online rule generation. The advantage of this algorithm is that the graph generated in our algorithm has less edge as compared to the lattice used in the existing algorithm. The Proposed algorithm generates all the essential rules also and no rule is missing. The use of non redundant association rules help significantly in the reduction of irrelevant noise in the data mining process. This graph theoretic approach, called adjacency lattice is crucial for online mining of data. The adjacency lattice could be stored either in main memory or secondary memory. The idea of adjacency lattice is to pre store a number of large item sets in special format which reduces disc I/O required in performing the query.