The blue noise mask (BNM) is a halftone screen that produces unstructured, visually pleasing halftone images. Since it is a point process, halftoning using the BNM can be implemented considerably faster than error diffusion and other algorithms. However, in the construction of the original BNM, a number of constraints were used to limit its characteristics in the spatial and frequency domains. These constraints were not efficient to compute and required adaptability to all gray levels in the construction process. The original BNM also contained some small but unwanted low-frequency components at some gray levels. In this paper, we present a revised approach to the generation of blue noise patterns and the construction of BNMs employing more efficient computations and eliminating more unwanted residual low-frequency components. Psychovisual evaluation shows that dithering with the new BNM gives excellent results and its rating is statistically indistinguishable from that of error diffusion with serpentine raster and perturbed weights.