  Let X be a smooth complex algebraic variety. In this paper, we associate, to
each exact n-cube of hermitian vector bundles over X, a differential form,
called higher Bott Chern form, which generalizes the Bott Chern forms
associated to an exact sequence of hermitian vector bundles. With these forms
we construct characteristic classes for higher K-theory and prove that these
classes agree with Beilinson's regulator. Thus we obtain a description of
Beilinson's regulator map in terms of hermitian vector bundles.
