In most applications four color printing is used to enlarge the printable color gamut especially in the dark color area. In this work we give a motivation for applying four color printing processes in order to achieve better color accuracy over different illuminants. For this reason we introduce a hypothetical four-dimensional observer whose four-dimensional color space can be completely addressed with four color printing.Finding the four colorant values of the printer for a desired four-dimensional color is done by color separation. We compare a color separation algorithm which is founded on the analytical inversion of the three-ink Neugebauer equations with a direct iterative inversion algorithm. Both approaches are shown to surely converge to the real valued colorant combination. The direct inversion requires no more than three iteration cycles.