A set D of a vertices in a graph G = (V,E) is said to be a total dominating set of G if every vertex in V is adjacent to some vertex in D. The total domination number t(G) is the minimum cardinality of a total dominating set. If t(G) 6 |V (G)|, the minimum cardinality of a set E0 ⊆ E(G), such that G − E0 contains no isolated vertices and t(G − E0) > t(G), is called the total bondage number of G. This paper determines the exact values of total bondage number of Wheel graph, Helm graph, Windmill graph, Circular necklace and Friendship graph.