  Within the nonrelativistic quantum chromodynamics (NRQCD) factorization
formalism, we compute the relativistic corrections to the exclusive decays of
bottomonia with even charge conjugation parity into $S$-wave charmonium pairs
at leading order in the strong coupling constant. Relativistic corrections are
resummed for a class of color-singlet contributions to all orders in the
charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process
that we consider in this work has negative relativistic corrections ranging
from -20 to -35,%. Among the various processes, the relativistic corrections of
the next-to-leading order in $v_c$ to the decay rate for $\chi_{b2}\to
\eta_c(mS)+\eta_c(nS)$ with $m,$ $n=1$ or 2 are very large. In every case, the
resummation of the relativistic corrections enhances the rate in comparison
with the next-to-leading-order results. We compare our results with available
predictions based on the NRQCD factorization formalism. The NRQCD predictions
are significantly smaller than those based on the light-cone formalism by an or
two orders of magnitudes.
