A new complex grinding method named Ultrasonic Electrodischarging Grinding Method (US-ED-G in short) is described. In the US-ED-G, ultrasonic grinding and ED grinding are simultaneously carried out on an electrically conductive workpiece with a metal bond grinding wheel. When compared with other complex grinding methods, the US-ED-G is remarkably effective in reducing grinding force a great deal and maintaining grinding ability of a wheel for a long time in efficient grinding of extremely hard-to-grind ceramic materials like TiB2. A stock removal rate of 200mm3/min and a grinding ratio of 110 have been attained by selecting appropriate conditions in US-ED-G of TiB2. A compact and rigid ultrasonic attachment is also described, which was developed as a removable tool for carrying out US grinding and US-ED-grinding on a machining center or a grinding center.