It was found that the model with interaction between cold dark matter (CDM) and dark energy (DE) proportional to the energy density of CDM ρ_m and constant equation of state of DE w_d suffered from instabilities of the density perturbations on the supper-Hubble scales. Here we suggest a new covariant model for the energy-momentum transfer between CDM and DE. Then using the covariant model, we analyze the evolution of density perturbations on the supper-Hubble scale. We find that the

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... s can be avoided in the model with constant w_d and interaction proportional to ρ_m. Furthermore, we analyze the dominant non-adiabatic mode in the radiation era and find that the mode grows regularly.