  We perform a self-consistent relativistic QRPA (RQRPA) calculation of
$2\nu\b\b$-decay based on relativistic BCS (RBCS) mean field theory results for
odd-odd intermediate nuclei $^{48}$Sc, $^{76}$As, $^{82}$Br, $^{100}$Tc,
$^{128}$I, and $^{130}$I. The RBCS equations that resemble the non-relativistic
ones are constructed from a Dirac-Gorkov variational functional. We use the
parameter set $NL1$ for the $\sigma$, $\omega$ and $\rho$ mesons. The RQRPA
equations are solved for the residual $\pi+\rho$ interaction by employing the
same parameters used in the RBCS for the latter meson, and experimental values
for the pion and nucleon. The RQRPA results for the ${2\nu}\b\b$ matrix
elements are similar to those obtained within the QRPA and the shell model.
