The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of ?-decay half-lives of neutron-rich nuclei in the N?50 and N?82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogoliubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains but overestimate the lifetimes of Ni isotopes and predict a stable 132Sn.