Hamiltonian index of a graph \(G\) is the smallest positive integer \(k\), for which the \(k\)-th iterated line graph \(L^k(G)\) is hamiltonian. Bedrossian characterized all pairs of forbidden induced subgraphs that imply hamiltonicity in \(2\)-connected graphs. In this paper, some upper bounds on the hamiltonian index of a \(2\)-connected graph in terms of forbidden not necessarily induced subgraphs are presented.