*

The study of the coupling between topological states of matter and correlated states such as superconductivity or density waves in quantum materials has been an active field of research in experimental condensed matter physics in recent years.  In this sense, TaTe₄, a representative of the family of transition metal tetrachalcogenides, appears as a perfect standpoint to study this kind of interplay, since it is a long known-charge density wave system and a predicted Weyl semi-metal. Here we present a detailed study of the electronic band structure of this compound, through a combination of high field magnetotransport measurements and density functional theory calculations. We provide evidence for the presence of Fermi surface sections not previously reported and analyze their connection with the predicted topological states for this compound.