  Let $D$ be a strongly connected balanced bipartite directed graph of order
$2a\geq 10$. Let $x,y$ be distinct vertices in $D$. $\{x,y\}$ dominates a
vertex $z$ if $x\rightarrow z$ and $y\rightarrow z$; in this case, we call the
pair $\{x,y\}$ dominating. In this paper we prove:
  {\it If the underlying undirected graph of $D$ is not 2-connected and
$max\{d(x), d(y)\}\geq 2a-2$ for every dominating pair of vertices $\{x,y\}$,
then
  $D$ contains a cycle of length $2a-2$ unless $D$ is isomorphic to a certain
digraph of order ten which we specify.
