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We propose a new operator for creating rotated dither threshold arrays. This new discrete one- to-one rotation operator is briefly explained. We analyze its application to different dispersed- dot dither arrays such as hexagonal dispersed dither arrays and 3X3 matrix-based Bayer- expanded dither arrays and compare the results with the ones obtained by rotating standard Bayer dither arrays. We show that the rotation operator introduced new lower-frequency components that, for example in the case of rotated dispersed-dot Bayer dither, produces a slight clustering effect, improving the tone reproduction behavior of the halftone patterns. In other cases, such as hexagonal dispersed dither, these new lower frequency components are responsible for strong interferences in the rotated halftone array. When applied to 3x3 matrix- based Bayer-expanded dither arrays, the rotation operator induces sequences of short horizontal and vertical patterns that have very good tone reproduction behavior in the dark tones. Besides their used in black and white printing, rotated dispersed-dot dither halftoning techniques have also been successfully applied to in-phase color reproduction on inkjet printers.