In previous works, a generic dynamical model has been suggested byHuang et al., which is shown to be correct for both adiabatic and radiative blast-waves, in both ultra-relativistic and non-relativistic phases. In deriving their equa-tions, Huang et al. have assumed that the radiative efficiency of the fireball isconstant. They then applied their model directly to realistic cases where the radia-tive efficiency evolves with time. In this paper, we abandon the above assumptionand re-derive a more accurate dynamical equation for gamma-ray burst remnants.Numerical results show that the model presented by Huang et al. is accurate enoughin general cases.