  It is well known that \textit{every} Eulerian orientation of an Eulerian
$2k$-edge connected (undirected) graph is strongly $k$-edge connected. An
important goal in the area is to obtain analogous results for other types of
connectivity, such as node connectivity and element connectivity. We show that
\textit{every} Eulerian orientation of the hypercube of degree $2k$ is strongly
$k$-node connected.
