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In this paper, we investigate a class of factorisable IC quasi-adequate semigroups,so-called, factorisable IC quasi-adequate semigroups of type-(H, I). Some characterizations of factorisable IC quasi-adequate semigroups of type-(H, I) are obtained. In particular, we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-(H, I) and a band of cancellative monoids.