We have investigated the thermal instability of Au(111) vicinal surfaces by scanning tunneling microscopy in ultrahigh vacuum. Above an annealing temperature of 700 K, both the Au(11,9,9) and the Au(4,3,3) surfaces undergo a phase separation into (111) facets and portions of (7,5,5). In addition, the faceted surfaces present a long-range order : the superperiod is 70 Angstrom for Au(11,9,9) and 110 Angstrom for Au(4,3,3). Large scale images show that this structure extends everywhere on the samples. It is demonstrated that the novel periodic morphology is an equilibrium state. Comparison is made with preliminary results of the Au(4,5,5) surface that belongs to the opposite zone. Observations suggest a dramatically different behavior : The surface phase separates into large (2,3,3) portions and a more complicated vicinal surface. The superperiod seems to be greater than 2000 Angstrom.