Phase shifting masks (PSMs) give us a breakthrough in the future semiconductor industry by extending sub-micron lithography further. PSM has been used for several years, and its requirements are changing due to the development of other technologies. First, it became possible to use high transmittance attenuated PSM (HT-Att-PSM) because of improvement in the photoresist technology. Second, continuous improvement in the technology of the inspection equipment lowered the inspection wavelength. Now, we are provisionally targeting to make HT-Att-PSM having 20% transmittance at ArF line and to choose KrF line as the inspection wavelength. In this study, we simulate the optimum conditions for HT-Att-PSM using matrix method. The simulation is performed to find the optimum range of the variables that yield 180 degree phase shift and 20 plus or minus 5% transmittance at the exposure wavelength, and less than 40% transmittance at the inspection wavelength. Based on the simulation results, we find the optimum fabrication condition of HT-Att-PSM. Using measured optical constants as a function of film composition, we determine the optimum film composition yielding 20% transmittance and 180 degree phase shift at the exposure wavelength and below 40% transmittance at the inspection wavelength. As a result, Cr2Al8O15 film with thickness of 124 nm was found to be suitable for ArF line HT- Att-PSM.