  Let ${[n] \choose k}$ and ${[n] \choose l}$ $( k > l ) $ where $[n] =
\{1,2,3,...,n\}$ denote the family of all $k$-element subsets and $l$-element
subsets of $[n]$ respectively. Define a bipartite graph $G_{k,l} = ({[n]
\choose k},{[n] \choose l},E)$ such that two vertices $S\, \epsilon \,{[n]
\choose k} $ and $T\, \epsilon \,{[n] \choose l} $ are adjacent if and only if
$T \subset S$. In this paper, we give an upper bound for the domination number
of graph $G_{k,2}$ for $k > \lceil \frac{n}{2} \rceil$ and exact value for
$k=n-1$.
