This paper presents a method for inferring species phylogenies using quartet inference under the coalescent model. The method, called SVDquartets, uses algebraic statistics and singular value decomposition (SVD) to estimate the phylogenetic relationship among quartets of taxa. It quantifies uncertainty using nonparametric bootstrapping and has been tested on simulated and empirical datasets. The method is computationally efficient and incorporates all sources of variability in the estimation process, including mutational and coalescent variance. It is applicable to both unlinked SNP data and multi-locus sequence data. The method was applied to datasets for Sistrurus rattlesnakes and soybeans, demonstrating its utility in species tree inference. The results show that the SVD score effectively identifies the valid split among four taxa, with high bootstrap support for the true phylogeny. The method is efficient and can be scaled to larger taxon sets using quartet assembly techniques. It is compared to other methods such as SNAPP and *BEAST, showing faster computation times and better performance in some cases. The method has potential to improve the set of tools available for species tree inference, as it directly uses sequence data and incorporates all sources of variability. However, further research is needed to address issues such as the number of quartets to sample and the estimation of other evolutionary parameters. The method is implemented in the software SVDquartets, which is available for download.This paper presents a method for inferring species phylogenies using quartet inference under the coalescent model. The method, called SVDquartets, uses algebraic statistics and singular value decomposition (SVD) to estimate the phylogenetic relationship among quartets of taxa. It quantifies uncertainty using nonparametric bootstrapping and has been tested on simulated and empirical datasets. The method is computationally efficient and incorporates all sources of variability in the estimation process, including mutational and coalescent variance. It is applicable to both unlinked SNP data and multi-locus sequence data. The method was applied to datasets for Sistrurus rattlesnakes and soybeans, demonstrating its utility in species tree inference. The results show that the SVD score effectively identifies the valid split among four taxa, with high bootstrap support for the true phylogeny. The method is efficient and can be scaled to larger taxon sets using quartet assembly techniques. It is compared to other methods such as SNAPP and *BEAST, showing faster computation times and better performance in some cases. The method has potential to improve the set of tools available for species tree inference, as it directly uses sequence data and incorporates all sources of variability. However, further research is needed to address issues such as the number of quartets to sample and the estimation of other evolutionary parameters. The method is implemented in the software SVDquartets, which is available for download.