  Let M be the moduli space of irreducible flat PSL(2,R) connections on a
punctured surface of finite type with parabolic holonomies around punctures. By
using a notion of admissibility of an ideal arc, M is covered by dense open
subsets associated to ideal triangulations of the surface. A principal bundle
over M is constructed which, when restricted to the Teichmuller component of M,
is isomorphic to the decorated Teichmuller space of Penner. The construction
gives a generalization to M of Penner's coordinates for the Teichmuller space.
