Recent studies, focused on dihedral angles and intersection processes, have increased understandings of conjugate fault mechanisms. We present new 3-D seismic data and microstructural core analysis in a case study of a large conjugate strike-slip fault system from the intracratonic Tarim Basin, NW China. Within our study area, "X" type NE and NW trending faults occur within Cambrian-Ordovician carbonates. The dihedral angles of these conjugate faults have narrow ranges, 19° to 62° in the Cambrian and 26° to 51° in the Ordovician, and their modes are 42° and 44° respectively. These data are significantly different from the ~60° predicted by the Coulomb fracture criterion. It is concluded that: (1) The dihedral angles of the conjugate faults were not controlled by confining pressure, which was low and associated with shallow burial; (2) As dihedral angles were not controlled by pressure they can be used to determine the shortening direction during faulting; (3) Sequential slip may have played an important role in forming conjugate fault intersections; (4) The conjugate fault system of the Tarim basin initiated as rhombic joints; these subsequently developed into sequentially active "X" type conjugate faults; followed by preferential development of the NW-trending faults; then reactivation of the NE trending faults. This intact rhombic conjugate fault system presents new insights into mechanisms of dihedral angle development, with particular relevance to intracratonic basins.