  We generalize the Serre-Swan theorem to non-commutative C$^{*}$-algebras. For
a Hilbert C$^{*}$-module $X$ over a C$^{*}$-algebra ${\cal A}$, we introduce a
hermitian vector bundle $\exx$ associated to $X$. We show that there is a
linear subspace $\Gamma_{X}$ of the space of all holomorphic sections of ${\cal
E}_{X}$ and a flat connection $D$ on ${\cal E}_{X}$ with the following
properties: (i) $\Gamma_{X}$ is a Hilbert ${\cal A}$-module with the action of
${\cal A}$ defined by $D$, (ii) the C$^{*}$-inner product of $\Gamma_{X}$ is
induced by the hermitian metric of ${\cal E}_{X}$, (iii) ${\cal E}_{X}$ is
isomorphic to an associated bundle of an infinite dimensional Hopf bundle, (iv)
$\Gamma_{X}$ is isomorphic to $X$.
