The dot diffusion method for digital halftoning has the advantage of parallelism unlike the error diffusion method. The method was recently improved by optimization of the so-called class matrix so that the resulting halftones are comparable to the error diffused halftones. In this paper we will first review the dot diffusion method. Previously, 8² class matrices were used for dot diffusion method. A problem with this size of class matrix is that enhancement of images is necessary before halftoning. However, enhancement may not be desirable in some applications. In order to eliminate the enhancement step, we increase the size of the class matrix to 16² and optimize the class matrix for a set of gray levels. In the optimization, the Human Visual System is used in the cost function. The optimization is done with the pairwise exchange algorithm. Since we increase the size of the class matrix, we are compromising the parallelism, i.e., the algorithm will terminate in 16² steps rather than 8 × 8 steps. This is the price paid for avoiding the enhancement step.