  The bunkbed of a graph $G$ is the graph $G\times K_2 $. It has been
conjectured that in the independent bond percolation model, the probability for
$\left(u,0\right)$ to be connected with $\left(v,0\right)$ is greater than the
probability for $\left(u,0\right)$ to be connected with $\left(v,1\right)$, for
any vertex $u$, $v$ of $G$. In this article, we prove this conjecture for the
complete graph in the case of the independent bond percolation of parameter
$p=1/2$.
