  We introduce C*-algebras over C_{\infty}(Q,C) as Banach-Kantorovich
*-algebras over the algebra C_{\infty}(Q,C) of extended continuous
complex-valued functions, defined on comeager subsets of Stonean compact Q,
whose norm satisfies conditions similar to the axioms of C*-algebras, and show
that such algebras can be uniquely up to a Q-C*-isomorphism represented by
means of a continuous complete fiber bundle of C*-algebras over Q.
