The layered ternary compound TaIrTe4 has been predicted to be a type-II Weyl semimetal with only four Weyl points just above the Fermi energy. Performing magnetotransport measurements on this material we find that the resistivity does not saturate for fields up to 70 T and follows a ρ∼B1.5 dependence. Angular-dependent de Haas-van Alphen measurements reveal four distinct frequencies. Analyzing these magnetic quantum oscillations by use of density functional theory calculations we establish that in TaIrTe4 the Weyl points are located merely ∼40-50 meV above the chemical potential.