Disclosed herein is a method and apparatus for moiré-free color halftone printing with up to five color image separations. The method and apparatus utilize a plurality of non-orthogonal halftone screens to produce outputs that are moiré free and form rosettes. The method and apparatus provide for defining a first and a second color halftone screen fundamental frequency vector for each of three halftone screens such that the halftone screen set output forms moiré-free rosettes; then defining a fourth color halftone screen where a first fundamental vector of the fourth screen shares a fundamental frequency vector with one of said three halftone screens and a second fundamental frequency vector of the fourth screen shares a fundamental frequency vector with a different one of said three color halftone screens; and further defining a fifth color halftone screen where a first fundamental vector of the fifth screen shares a fundamental frequency vector with one of said three halftone screens and a second fundamental frequency vector of the fifth screen shares a fundamental frequency vector with a different one of said three color halftone screens, and the neither of the fundamental frequency vectors of the fifth screen are equal to either of the fundamental frequency vectors of the fourth screen.