In recent years, non-contact ratiometric luminescence thermometry has continued to gain popularity among researchers, owing to its compelling features, such as high accuracy, fast response, and convenience. The development of novel optical thermometry with ultrahigh relative sensitivity (Sr) and temperature resolution has become a frontier topic. In this work, we present a novel, to the best of our knowldege, luminescence intensity ratio (LIR) thermometry method that relies on AlTaO4:Cr3+ materials, based on the fact that they possess both anti-Stokes phonon sideband emission and R-line emission at the 2E→4A2 transitions and have been confirmed to follow the Boltzmann distribution. In the temperature range 40-250 K, the emission band of the anti-Stokes phonon sideband shows an upward trend, while the bands of the R-lines show the opposite downward trend. Relying on this fascinating feature, the newly proposed LIR thermometry achieves a maximum relative sensitivity of 8.45%K-1 and a temperature resolution of 0.038 K. Our work is expected to provide guiding insights for optimizing the sensitivity of Cr3+-based LIR thermometers and provide some novel entry points for designing excellent and reliable optical thermometers.