In contrast to high-statistics antiproton ($\bar{p}$) measurements, no cosmic-ray
antideuteron ($\bar{d}$) has been detected. An advantage of the $\bar{d}$ search over the
$\bar{p}$ measurement lies in the extremely low astrophysical background of
$\bar{d}$'s, especially at low energy. Before the flight of the next-generation
experiment, GAPS, we searched for $\bar{d}$'s in the $4.7 \times 10^{9}$ cosmic-ray events
observed by BESS-Polar II at the solar minimum in 2007. No $\bar{d}$ candidates
were detected in the analysis, which adapted a quality cut nearly identical to the
BESS-Polar II $\bar{p}$ flux calculation. Thus, the 95\% C.L. upper limit on
the $\bar{d}$ flux in the energy range from 0.163 to 1.100 GeV/n at the top
of the atmosphere was calculated with a conservative analysis.
The resultant upper limit was compared to BESS97-00, which currently has the best
sensitivity for searching for cosmic-origin $\bar{d}$'s of
$1.9 \times 10^{-4}$ $\rm (m^{2}~s~sr~GeV/n)^{-1}$
and several theories. We will report details of the analysis and the upper limit
on $\bar{d}$ flux with BESS-Polar II.