Since the introduction of the automated karyotyping systems, segmentation and classification of touching and overlapping chromosomes in the metaphase images are major challenges. The earlier reported techniques for disentangling the chromosome overlaps have limited success and use only color information in case of multispectral imaging. Most of them are restricted to separation of single overlap of two chromosomes. This paper introduces a novel algorithm to extricate overlapping chromosomes in a metaphase image. The proposed technique uses Delaunay triangulation to automatically identify the number of overlaps in a cluster followed by the detection of the appropriate cut-points. The banding information on the overlapped region further resolves the set of overlapping chromosomes with the identified cut-points. The proposed algorithm has been tested with four data sets of 60 overlapping cases, obtained from publically available databases and private genetic labs. The experimental results provide an overall accuracy of 75–100 % for resolving the cluster of 1–6 overlaps.