AbstractRecent 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.