Radiative instabilities in an impurity-seeded plasma are investigated when the plasma is supposed to be highly but partially ionized. Since in such plasmas radiative losses strongly depend on neutral and impurity densities, their dynamics are taken into account. As a result, a new radiative-recombination instability is found and described. We show that the influence of the ionization-recombination balance on plasma stability is sufficient for plasma densities above 1014 cm-3. The effects of a finite impurity Larmor radius are not small and play a stabilizing role as well as the thermal forces. On the other hand, compressibility of the magnetic field leads to plasma destabilization. We note that this radiative-recombination instability accumulates impurities in a cold zone while cleaning other regions.