A novel RET, which enables on-grid sub-50 nm hole pattern formation with ArF immersion lithography, has been developed. One of the authors has found quasi-iso-focal point image generation at the center of square area of high transmission embedded attenuating phase shift mask (EA-PSM), where four small openings are laid out at the corners of the area, utilizing an optimized quadrupole illumination. As an extension of continuous configuration, checker-board like mask pattern arrangement is created. In the mask, small openings and opaque pads are arranged like as checkerboard, whose base pitch is around resolution limit of targeted optical system. The mask pattern arrangement is named as "Checker-Board PSM (CB-PSM)". By eliminating any one opening from "checker-board", very fine point image is generated at the place. Because four openings around the eliminated one are necessary for the fine imaging characteristic, minimum distance between the point images is about the double of that for resolution limit. After simulation study of imaging, experiments are carried out to prove the fine imaging performance utilizing ArF immersion optics with NA=1.07 and a tri-level resist system. As a result, sub-50nm isolated hole is successfully formed with DOF larger than 200 nm. Simultaneously, ~ 60 nm semi-dense hole with pitch of 240 nm is printed with over 200 nm DOF. Moreover, application of conventional mask pattern arrangement, ultimately dense hole of 140nm pitch is well formed. As a conclusion, we believe that CB-PSM is a promising candidate for hole pattern formation at 32 nm node and beyond.