  We construct some analog of cubical Bloch's higher Chow groups. Instead of
considering cycles in $X\times\mathbb A^n$ we consider varieties $Y$ over $X$
together with a distinguished element in the $n$-th exterior power of the
multiplicative group of the field of fraction on $Y$. This definition allows us
to make sense of a cycle in $X\times\mathbb A^n$ intersecting faces improperly
as an element in this complex.
  We prove that this complex is well-defined and study its basic properties:
flat pullback, the localization sequence etc. As an application we prove that
the cohomology of this complex in degrees $m-1, m$ and weight $m$ isomorphic to
the cohomology of polylogarithmic complex.
