  In this paper, we study $(1,2)$-step competition graphs of bipartite
tournaments. A bipartite tournament means an orientation of a complete
bipartite graph. We show that the $(1,2)$-step competition graph of a bipartite
tournament has at most one non-trivial component or consists of exactly two
complete components of size at least three and, especially in the former, the
diameter of the nontrivial component is at most three if it exists. Based on
this result, we show that, among the connected non-complete graphs which are
triangle-free or the cycles of which are edge-disjoint, $K_{1,4}$ is the only
graph that can be represented as the $(1,2)$-step competition graph of a
bipartite tournament. We also completely characterize a complete graph and the
disjoint union of two complete graphs, respectively, which can be represented
as the $(1,2)$-step competition graph of a bipartite tournament. Finally we
present the maximum number of edges and the minimum number of edges which the
$(1,2)$-step competition graph of a bipartite tournament might have.
