  The orientation theorem of Nash-Williams states that an undirected graph
admits a $k$-arc-connected orientation if and only if it is
$2k$-edge-connected. Recently, Ito et al. showed that any orientation of an
undirected $2k$-edge-connected graph can be transformed into a
$k$-arc-connected orientation by reorienting one arc at a time without
decreasing the arc-connectivity at any step, thus providing an algorithmic
proof of Nash-Williams' theorem. We generalize their result to hypergraphs and
therefore provide an algorithmic proof of the characterization of hypergraphs
with a $k$-hyperarc-connected orientation originally given by Frank et al. We
prove that any orientation of an undirected $(k,k)$-partition-connected
hypergraph can be transformed into a $k$-hyperarc-connected orientation by
reorienting one hyperarc at a time without decreasing the hyperarc-connectivity
in any step. Furthermore, we provide a simple combinatorial algorithm for
computing such a transformation in polynomial time.
