An improved ray tracing air mass model to calculate the air mass numbers for the entire zenith angle range is developed. The improved model uses the approach when the trajectory element of light in the atmosphere is approximated by an arc of a circle. This way the angles at the beginning and at the end of the trajectory element can be counted simultaneously. This approach gives the second-order approximation for the real light trajectory with more accurate results than the results of the approaches of Link and Neuzil (Tables of Light Trajectories in the Terrestrial Atmosphere, Hermann, 1969) and the Kasten and Young models [Appl. Opt. 28, 4735 (1989)]. The developed model allows us to avoid the calculation problems of the Link and Neuzil and Kasten models when the zenith angle is close to or equal to 90°. As a result, we deliver the new air mass number table for the entire zenith angle range and provide the comparison of the developed model results with the results of the Link and Neuzil and the Kasten models.