The invention relates to a method and apparatus for automatic high-speed generation of digital angled halftone screens, specially suited for obtaining screens approximating the irrational angles which are generally required by high-quality colour reproduction. The method enables colour separations to be generated which minimize Moire effects, interferences and artifacts by applying discrete one-to-one rotations to digital halftone screens of the required period in order to reach the final screen angle. Dither tiles incorporating assemblies of the basic screen element are rotated by one-to-one discrete rotation and transformed into a new type of dither array, the scanning dither array. The scanning dither array is composed both of dither thresholds and of displacement vectors, providing the means to scan the dither array at image generation time. Several different discrete one-to-one rotation variants are proposed: a small angle rotation technique valid for a subset of rational rotation angles, a rigid band technique and an improved band technique valid for all rational rotation angles and a technique based on discrete shearing transformations. The high- quality of the so rotated dither tile is due to the fact that discrete one-to-one rotation preserves the exact number of elementary cells per screen element and their exact dither threshold values. Since discrete one-to-one rotation enables screen tiles generated by any existing or new method to be rotated, it provides a new range of solutions for obtaining high-quality digital angled halftone screens. In this range of solutions, high-quality solutions can be found for generating three digital angled halftone screens, each 30 deg. apart from each other, as known from traditional photographic colour screening techniques. Further solutions minimizing Moire effects may be obtained by halftone screens whose first order frequency component vectors sum up to zero. Since most of the proposed discrete one-to-one rotation variants can be accomplished by simple and incremental operations such as additions, subtractions, shifts, replications and table accesses, discrete one-to-one rotation is capable of generating angled halftone screens at high-speed. The invented process has turned out to be particularly effective when printing with color ink jet printers at resolutions between 150 and 800 dpi as well as with xerographic printers at resolutions between 300 and 1200 dpi.