Fault attributes generally display a consistent power–law-scaling relationship. Based on new 3D seismic data, however, we found some exceptional fault attribute relationships of lengths (L)–throw (T) (vertical component of displacement), overlap zone length (Lo)–width (Wo) from a strike-slip fault system of the Ordovician carbonates in the Tarim Basin. The L–T relationship shows two linear segments with breakup at ~40 km in fault length. This presents an exceptional throw increase in the second stage, which is attributed to a localization of vertical displacement and deformation in overlapping zones other than the different fault scales in a mature fault zone. The Lo–Wo relationship in the overlapping zones shows multiply stepped-shape patterns, suggesting multiple fault differential growth and periodic increase in fault size. Therefore, we propose a new alternative growth model of fault attributes in strike-slip fault zones, in which the overlapping zones accumulated localized displacement and deformation in the intracratonic strike-slip fault zone.