  Let $V$ denote a vector space with finite positive dimension. We consider an
ordered pair of linear transformations $A: V\rightarrow V$ and $A^*:
V\rightarrow V$ that satisfy (i) and (ii) below.
  (i) There exists a basis for $V$ with respect to which the matrix
representing $A$ is irreducible tridiagonal and the matrix representing $A^*$
is diagonal.
  (ii) There exists a basis for $V$ with respect to which the matrix
representing $A^*$ is irreducible tridiagonal and the matrix representing $A$
is diagonal.
  We call such a pair a Leonard pair on $V$. Very roughly speaking, a Leonard
pair is a linear algebraic abstraction of a $Q$-polynomial distance-regular
graph. There is a well-known class of distance-regular graphs said to be
bipartite and there is a related notion of a bipartite Leonard pair. Recently,
M. S. Lang introduced the notion of a tail for bipartite distance-regular
graphs, and there is an abstract version of this tail notion. Lang
characterized the bipartite $Q$-polynomial distance-regular graphs using tails.
In this paper, we obtain a similar characterization of the bipartite Leonard
pairs using tails. Whereas Lang's arguments relied on the combinatorics of a
distance-regular graph, our results are purely algebraic in nature.
