Discrete line juxtaposed halftoning creates color halftones with discrete colorant lines of freely selectable rational thicknesses laid-out side by side. Screen elements are made of parallelogram screen tiles incorporating the discrete colorant lines. The repetition of discrete colorant lines from one screen element to the next may create auto moiré artifacts. By decomposing each supertile into screen element tiles having slightly different rational thicknesses, we ensure that successive discrete colorant lines have different phases in respect to the underlying pixel grid. The resulting repetition vector is different from one discrete line to the next discrete line of the same colorant. This strongly reduces the original auto moiré artifacts.