The ordinary dielectric function (DF) is presented for high quality Al-rich Al1−xInxN alloy films pseudomorphically grown on GaN in the photon energy range 1–18 eV determined by spectroscopic ellipsometry at room temperature (synchrotron radiation – BESSY II). The (0001)-oriented layers with In content of 14.3 and 15.4% were grown by metal-organic vapour phase epitaxy on thick GaN buffers with sapphire substrates. The sharp onset of the imaginary part of the DF defines the direct absorption edge. In previous studies the DF of Al-rich AlInN were investigated in the photon energy range 1–10 eV, and three high-energy critical points (CPs) of the band structure (Van Hove singularities) were observed. The current study was performed in the extended photon energy range 10–18 eV and three CPs of the band structure at ∼10.6, ∼12.5 and ∼14.2 eV were detected. XRD measurements revealed the pseudomorphic growth of AlInN films and yielded the composition. Finally, the band gap value of 4.68 eV and high-frequency dielectric constant value of 4.55 were evaluated for sample with 15.4% In content.