Myriapods, a diverse group of terrestrial arthropods, comprise four main subgroups: Chilopoda (centipedes), Diplopoda (millipedes), Pauropoda, and Symphyla. Recent phylogenomic studies affirm Myriapoda's monophyly and the monophyletic status of each subgroup but differ in their relationships. To investigate these relationships further, we reanalyzed a transcriptomic dataset of 59 species across 292 single-copy protein-coding genes. Departing from conventional methods, we employed a novel approach that relies on information from polarized quartets (i.e., sets of four orthologous sequences, with one being an outgroup) to evaluate molecular phylogenies. This Hennigian analysis reduces misleading phylogenetic signals in molecular data caused by convergence, plesiomorphy, and rate heterogeneity across sites and across lineages. Our findings reveal that some species, especially those with long root-to-tip distances, disproportionately contribute misleading signals. Analyses using conventional likelihood-based phylogenetic methods suggest that Chilopoda and Diplopoda are sister taxa. By contrast, analyses incorporating novel filters designed to minimize conflict among phylogenetically confounding signals support the monophyly of Progoneata, aligning with morphological evidence. Simulations validate the reliability of our approach, demonstrating its potential to resolve myriapod evolutionary relationships and highlight uncertainty.