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Let $ G $ be a graph. A subset $S \subseteq V(G) $ is called a totaldominating 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 cardinalityof a total dominating set of $G$. In this paper using a greedy algorithm weprovide an upper bound for $\gamma_{t}$($G$), whenever $G$ is a bipartite graphand $\delta(G)$ $\geq$ $k$. More precisely, we show that if $k$ > 1 is anatural number, then for every bipartite graph $G$ of order $n$ and $\delta(G)\ge k$, $ $$\gamma_{t}$($G$) $\leq$ $n(1-\frac{k!}{\prod_{i=0}^{k-1}(\frac{k}{k-1}+i)}).$

A New Upper Bound on Total Domination Number of Bipartite Graphs