Let A be a commutative C* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to C0(G), the C* -algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the case of Hopf C* -algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C* -algebra are proposed.