In June 2015, Cassini high-resolution images of Saturn's limb southwards of the planet's hexagonal wave revealed a system of at least six stacked haze layers above the upper cloud deck. Here, we characterize those haze layers and discuss their nature. Vertical thickness of layers ranged from 7 to 18km, and they extended in altitude similar to 130km, from pressure level 0.5bar to 0.01bar. Above them, a thin but extended aerosol layer reached altitude similar to 340km (0.4mbar). Radiative transfer modeling of spectral reflectivity shows that haze properties are consistent with particles of diameter 0.07-1.4 mu m and number density 100-500cm(-3). The nature of the hazes is compatible with their formation by condensation of hydrocarbon ices, including acetylene and benzene at higher altitudes. Their vertical distribution could be due to upward propagating gravity waves generated by dynamical forcing by the hexagon and its associated eastward jet. The authors analyze a system of multi-layered hazes above Saturn's hexagonal-wave cloud tops in the visual range. Analyses suggest the formation to be caused by condensation processes, and the vertical distribution of stacked layers by the upward propagation of internal gravity waves.