The quantum chromodynamics with massless quarks and an infinite number of colors is represented as a theory of the noninteracting mesons which lie on rising Regge trajectories. The perturbation theory for these trajectories is developed. The expansion parameter (effective coupling) is calculated and appears to be about 1/2. The expansion coefficients can also be calculated analytically as functions of spin and other quantum numbers. The calculations are carried through to the end in the zeroth and first order. The resulting trajectories look reasonable and are in qualitative agreement with experiment. The corrections from finite numbers of colors and from quark masses can also be found, but are not considered here.