  Let $ G $ be a graph. A subset $S \subseteq V(G) $ is called a total
dominating set if every vertex of $G$ is adjacent to at least one vertex of
$S$. The total domination number, $\gamma_{t}$($G$), is the minimum cardinality
of a total dominating set of $G$. In this paper using a greedy algorithm we
provide an upper bound for $\gamma_{t}$($G$), whenever $G$ is a bipartite graph
and $\delta(G)$ $\geq$ $k$. More precisely, we show that if $k$ > 1 is a
natural number, then for every bipartite graph $G$ of order $n$ and $\delta(G)
\ge k$, $ $$\gamma_{t}$($G$) $\leq$ $n(1-
\frac{k!}{\prod_{i=0}^{k-1}(\frac{k}{k-1}+i)}).$
