  Let $n$ and $k$ be integers with $n>2k, k\geq1$. We denote by $H(n, k)$ the
$bipartite\ Kneser\ graph$, that is, a graph with the family of $k$-subsets and
($n-k$)-subsets of $[n] = \{1, 2, ... , n\}$ as vertices, in which
  any two vertices are adjacent if and only if one of them is a subset of the
other. In this paper, we determine the automorphism group of $H(n, k)$. We show
that $Aut(H(n, k))\cong Sym([n]) \times \mathbb{Z}_2$ where $\mathbb{Z}_2$ is
the cyclic group of order $2$. Then, as an application of the obtained result,
we give a new proof for determining the automorphism group of the Kneser graph
$K(n,k)$. In fact we show how to determine the automorphism group of the Kneser
graph $K(n,k)$ given the automorphism group of the Johnson graph $J(n,k)$. Note
that the known proofs for determining the automorphism groups of Johnson graph
$J(n,k)$ and Kneser graph $ K(n,k)$ are independent from each other.
