  We show that the infinite-dimensional Teichmueller space of a Riemann surface
whose boundary consists of n closed curves is a holomorphic fiber space over
the Teichmueller space of n-punctured surfaces. Each fiber is a complex Banach
manifold modeled on a two-dimensional extension of the universal Teichmueller
space. The local model of the fiber, together with the coordinates from
internal Schiffer variation, provides new holomorphic local coordinates for the
infinite-dimensional Teichmueller space.
