  It was found that the model with interaction between cold dark matter (CDM)
and dark energy (DE) proportional to the energy density of CDM $\rho_m$ 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 instabilities can be avoided in the model
with constant $w_d$ and interaction proportional to $\rho_m$. Furthermore, we
analyze the dominant non-adiabatic mode in the radiation era and find that the
mode grows regularly.
