  A new compactification for the scheme of moduli for Gieseker-stable vector
bundles with prescribed Hilbert polynomial, on the smooth projective polarized
surface (S,L), is constructed. Families of locally free sheaves on the surface
S are completed by locally free sheaves on schemes which are modifications of
S. Gieseker -- Maruyama moduli space has a birational morphism onto the new
moduli space. We propose the functor for families of pairs polarized scheme --
vector bundle with moduli space of such type.
