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.