  It is found that the evolutions of density perturbations on the super-Hubble
scales are unstable in the model with dark-sector interaction $Q$ proportional
to the energy density of cold dark matter (CDM) $\rho_m$ and constant equation
of state parameter of dark energy $w_d$. In this paper, to avoid the
instabilities, we suggest a new covariant model for the energy-momentum
transfer between DE and CDM. Then we show that the the large-scale
instabilities of curvature perturbations can be avoided in our model in the
universe filled only by DE and CDM. Furthermore, by including the additional
components of radiation and baryons, we calculate the dominant non-adiabatic
modes in the radiation era and find that the modes grow in the power law with
exponent at the order of unit.
