Rotation–vibration coupling parameter b at different spins is calculated on fitting the experimental energy for each nucleus in the framework of the General Asymmetric Rotor Model (Zhi. Phys. Rev. C, 51, 141 (1995)). Taking the even and odd spin energy sequences of the gamma band as separate bands besides the yrast band at large asymmetry (γ ≥ 20°), three values of the moment of inertia parameters a (ar, ae, and ao) are calculated from the band head energies. A striking correlation in a and b versus the product of the number of valance protons and neutrons (NpNn) is obtained. These trajectories and the γ versus NpNn correlation (Yan et al. Phys. Rev. C, 48, 1046 (1993)) are capable of predicting the unknown energies of the ground and gamma bands of even xenon and barium nuclei, knowing only an external parameter NpNn. This introduces the possibility of a simpler description of the structural evolution of these transitional nuclei.