Low-lying isomers of homoleptic gold thiolate clusters (AuSR)(N) (N = 6-12) are studied by using a global-minimum search method. Besides previously known zigzag crown structures for (AuSR)(N) (N = 6-12) and catenane structures for (AuSR)(N) (N = 10, 12), onset of a new structural family of double helical structures in small-sized gold thiolate clusters and the separate-ring structures in larger clusters is revealed. At N = 6-9, the double helical structures are predicted to be the global minima. The onset of double helical structures suggests a new folding way for flexible gold thiolate clusters. The simulated UV-vis spectra and XRD patterns for all low-lying clusters are ready to compare with future experiments.