Mitochondrial DNA (mtDNA) sequences are comonly used for inferring phylogenetic relationships. However, the strand-specific bias in the nucleotide composition of the mtDNA, which is thought to reflect assymetric mutational constraints, combined with the important compositional heterogeneity among taxa, are known to be highly problematic for phylogenetic analyses. Here, nucleotide composition was compared across 49 species of Metazoa (34 arthropods, 2 annelids, 2 molluscs, and 11 deuterosomes), and analyzed for a mtDNA fragment including six protein-coding genes, i.e., atp6, atp8, cox1, cox2, cox3, and nad2. The analyses show that most metazoan species present a clear strand assymetry, where one strand is biased in favor of A and C, whereas the other strand has reverse bias, i.e. in favor of T and G. the origin of this strand bias can be related to assymetric mutational constraints involving deaminations of A and C nucleotides during the replication and/or transcription processes. The analyses reveal that six unrelated genera are characterized by a reversal of the usual strand bias, i.e., Argiope (Araneae), Euscorpius (Scorpiones), Tigrioupus (Maxillopoda), Branchiostoma (Cephalochordata) Florometra (Echinodermata), and Katharina (Mollusca). It is proposed that assymetric mutational constraints have been independantly reversed in these six genera, through an inversion of the control region, i.e., the region that contains most regulatory elements for replication and transcription of the mtDNA. We show that reversals of assymetric mutational constraints have dramatic consequences on the phylogenetic analyses, as taxa characterized by reverse strand bias tend to group together due to long-branch attraction artifacts. We propose a new method for limiting this specific problem in tree reconstruction under the Bayesian approach. We apply our method to deal with the question of phylogenetic relationships of the major lineages of Arthropoda, This new approach provides a better congruence with nuclear analyses based on mtDNA sequences, our data suggest that Chelicerata, Crustacea, Myriapoda, Pancrustacea, and Paradoxopoda are monophyletic.