  We present a search for the rare flavour-changing neutral-current decay
$B^{-}\to K^{-} \nu \bar{\nu}$ based on a sample of $(86.9 \pm 1.0) \times
10^{6}$ $\Upsilon (4S) \to $B\bar{B}$ events collected by the BABAR experiment
at the SLAC B-factory. Signal candidate events are selected by fully
reconstructing a $B^+ \to \bar{D}^{0} X^+$ decay, where $X^+$ represents a
combination of up to three charged pions or kaons and up to two $\pi^0$
candidates. The charged tracks and calorimeter clusters not used in the $B^+$
reconstruction are required to be compatible with a $B^{-}\to K^{-} \nu
\bar{\nu}$ decay. We observe a total of three signal candidate events with an
expected background of $2.7 \pm 0.8$, resulting in a preliminary limit of
$\mathcal{B}(B^{-}\to K^{-} \nu \bar{\nu}) < 1.05 \times 10^{-4}$ at the 90%
confidence level. This search is combined with the results of a previous and
statistically independent preliminary BABAR search for $B^{-}\to K^{-} \nu
\bar{\nu}$ to give a limit of $\mathcal{B}(B^{-}\to K^{-} \nu \bar{\nu}) < 7.0
\times 10^{-5}$ at the 90% confidence level.
