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Rooted species trees are used in several downstream applications of phylogenetics. Most species tree estimation methods produce unrooted trees and additional methods are then used to root these unrooted trees. Recently, Quintet Rooting (QR) (Tabatabaee et al., ISMB and Bioinformatics 2022), a polynomial-time method for rooting an unrooted species tree given unrooted gene trees under the multispecies coalescent, was introduced. QR, which is based on a proof of identifiability of rooted 5-taxon trees in the presence of incomplete lineage sorting, was shown to have good accuracy, improving over other methods for rooting species trees when incomplete lineage sorting was the only cause of gene tree discordance, except when gene tree estimation error was very high. However, the statistical consistency of QR was left as an open question. Here, we present QR-STAR, a polynomial-time variant of QR that has an additional step for determining the rooted shape of each quintet tree. We prove that QR-STAR is statistically consistent under the multispecies coalescent model, and our simulation study shows that QR-STAR matches or improves on the accuracy of QR. QR-STAR is available in open source form at https://github.com/ytabatabaee/Quintet-Rooting.