Currently, much attention is being paid to patterned multilayer systems in which there exists a perpendicular magnetic anisotropy, because of their potential applications in spintronics devices and in a new generation of magnetic storage media. To further improve their performance, different patterning techniques can be used, which render them suitable also for other applications. Here we show that He(+) 10 keV and Ar(+) 100 keV ion bombardment of (Ni(80)Fe(20)-2 nm/Au-2 nm/Co-0.6 nm/Au-2 nm)(10) multilayers through colloidal mask enables magnetic patterning of regularly arranged cylindrical magnetic domains, with perpendicular anisotropy, embedded in a non-ferromagnetic matrix or in a ferromagnetic matrix with magnetization oriented along the normal. These domains form an almost perfect two-dimensional hexagonal lattice with a submicron period and a large correlation length in a continuous and flat multilayer system. The magnetic anisotropy of these artificial domains remains unaffected by the magnetic patterning process, however the magnetization configuration of such a system depends on the magnetic properties of the matrix. The micromagnetic simulations were used to explain some of the features of the investigated patterned structures.