  Let $J_G$ denote the binomial edge ideal of a connected undirected graph on
$n$ vertices. This is the ideal generated by the binomials $x_iy_j - x_jy_i,
1\leq i < j \leq n,$ in the polynomial ring $S= K[x_1,...,x_n,y_1,...,y_n]$
where $\{i,j\}$ is an edge of $G$. We study the arithmetic properties of
$S/J_G$ for $G$, the complete bipartite graph. In particular we compute
dimensions, depths, Castelnuovo-Mumford regularities, Hilbert functions and
multiplicities of them. As main results we give an explicit description of the
modules of deficiencies, the duals of local cohomology modules, and prove the
purity of the minimal free resolution of $S/J_G$.
