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Summary form only given. We previously presented a new fingerprint core detection methodology using an extended relational graph, which is generated by the segmentation of the ridge directional image. That approach concerned only detecting the fingerprint core. This paper describes an improvement to that method, which can detect not only the core location, but also the delta location; a modification is applied to find both the core loop and the delta loop in the extended relational graph. Furthermore, to reduce the computation time, each difference of the ridge direction on the boundary along the loop is used to detect the fingerprint core, except the approximated straight lines generated by the boundary information in the extended relational graph. The experimental results for 224 fingerprint samples show that an average of 6% reduction of the processing time is achieved. 95.6% of cores and deltas can be detected successfully.