Disclosed herein is a method and apparatus for moiré-free enhanced color halftone printing of color image separations for an arbitrary number of colorants. The method and apparatus utilizes a plurality of halftone screens, >4, to produce outputs that are moiré free and form hexagonal periodic rosettes. The relatively large number of screens can be used for enhanced printing applications, such as printing with high-fidelity colorants, light colorants, or special colorants, such as white, metallics and fluorescents. The method and apparatus provide for defining rosette fundamental frequency vectors VR1, VR2 that satisfy a length and sum requirement to meet visual acceptability standards according to |VR1|>fmin, |VR2|>fmin, and |VR1±VR2|>fmin; defining N halftone screens for colorants i=1, N, respectively possessing first and second frequency vectors (Vi1, Vi2), where no two screens possess identical fundamental frequency vector pairs; and selecting fundamental frequency vectors for the N halftone screens according to (Vi1, Vi2)=(mi1VR1+mi2VR2, ni1VR1+ni2VR2) for integer m's and n's, where at least one fundamental frequency vector or its conjugate must also satisfy one of the following: Vik=VR1, Vik=VR2, and |Vik>2 max [|VR1|, |VR2|].