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Fault localization, aiming at localizing the root cause of the bug under repair, has been a longstanding research topic. Although many approaches have been proposed in the last decades, most of the existing studies work at coarse-grained statement or method levels with very limited insights about how to repair the bug (granularity problem), but few studies target the finer-grained fault localization. In this paper, we target the granularity problem and propose a novel finer-grained variable-level fault localization technique. Specifically, we design a program-dependency-enhanced decision tree model to boost the identification of fault-relevant variables via discriminating failed and passed test cases based on the variable values. To evaluate the effectiveness of our approach, we have implemented it in a tool called VARDT and conducted an extensive study over the Defects4J benchmark. The results show that VARDT outperforms the state-of-the-art fault localization approaches with at least 247.8% improvements in terms of bugs located at Top-1, and the average improvements are 330.5%. Besides, to investigate whether our finer-grained fault localization result can further improve the effectiveness of downstream APR techniques, we have adapted VARDT to the application of patch filtering, where VARDT outperforms the state-of-the-art PATCH-SIM by filtering 26.0% more incorrect patches. The results demonstrate the effectiveness of our approach and it also provides a new way of thinking for improving automatic program repair techniques.