  We analyse the eigenvalues of Erd\"os--R\'enyi random bipartite graphs. In
particular, we consider $p$ satisfying
$n_{1}p=\Omega(\sqrt{n_{1}p}\log^{3}(n_{1})),$
$n_{2}p=\Omega(\sqrt{n_{2}p}\log^{3}(n_{2})),$ and let $G\sim
G(n_{1},n_{2},p)$. We show that with probability tending to $1$ as $n_{1}$
tends to infinity: $$\mu_{2} (A(G))\leq
2[1+o(1)](\sqrt{n_{1}p}+\sqrt{n_{2}p}+\sqrt{(n_{1}+n_{2})p}).$$
