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The use of single nucleotide polymorphisms (SNPs) has become increasingly important for a wide range of genetic studies. A high-throughput genotyping technology usually involves a statistical algorithm for automatic (non-manual) genotype calling. Most calling algorithms in the literature, using methods such as k-means and mixture-models, rely on elliptical structures of the genotyping intensity data. They may fail when the intensity data have linear patterns. We propose an automatic genotype calling algorithm by further developing a linear grouping algorithm (LGA). The proposed method clusters data points around lines as opposed to around centroids. The clusters are on lines because we do not normalize the intensities. In addition, we associate a quality value, silhouette width, with each DNA sample and with each whole plate. For a data set of 101 SNPs from the TaqMan platform (Applied Biosystems), the LGA algorithm has 100% automatic calling and 93% of samples pass a quality criterion and are assigned a genotype. For a subset of 30 SNPs where validated samples are available, the accuracy for called genotypes is over 98%. Thus, a key feature of applying LGA to unnormalized TaqMan SNP assay fluorescent signals is that it is able to call automatically and realiably a substantial proportion of samples, reducing the need for manual intervention. It could be potentially adapted to other fluorescent-based SNP genotyping technologies such as Invader Assay.