Summary: A graph \(G\) is called a totally irregular total \(k\)-graph if it has a totally irregular total \(k\)-labeling \(\lambda : V \cup E \rightarrow \{1, 2, \dots, k\}\), that is a total labeling such that for any pair of different vertices \(x\) and \(y\) of \(G\), their weights \(wt(x)\) and \(wt(y)\) are distinct, and for any pair of different edges \(e\) and \(f\) of \(G\), their weights \(wt(e)\) and \(wt(f)\) are distinct. The minimum value \(k\) under labeling \(\lambda\) is called the total irregularity strength of \(G\), denoted by \(ts(G)\). For special cases of a complete bipartite graph \(K_{m, n}\), the \(ts(K_{1,n}\) and the ts \((K_{n, n})\) are already determined for any positive integer \(n\). Completing the results, this paper deals with the total irregularity strength of complete bipartite graph \(K_{m, n}\) for any positive integer \(m\) and \(n\).