  We study the production of antineutrinos from the solar neutrinos due the
Majorana neutrino decays of neutrino to antineutrino. Using the antineutrino
spectra from KamLAND and Borexino, we present newest limits on the lifetime of
$\nu_{3}$ in this scenario. We consider $\nu_{3} \rightarrow \bar{\nu}_{1} + X$
and $\nu_{3} \rightarrow \bar{\nu}_{2} + X$ channels assuming scalar or
pseudo-scalar interactions. For hierarchical mass-splittings, the limits
obtained by us are $\tau_{3}/m_{3}~\geq 7\times 10^{-5} s/eV$ and
$\tau_{3}/m_{3}~\geq 1\times 10^{-5} s/eV$ for the two channels at $90\%$ C.L.
We found that the newest bound is five orders of magnitude better than the
atmospheric and long-baseline bounds.
