use of the aforesaid grinding apparatus 1 to make the frictional surface flatter in this grinding process it is possible to obtain the flat surface as desired the state of which is shown in fig6 c after these processes large irregularities are removed almost completely in accordance with the present invention that has been described above it is possible to obtain the following effects with the present invention cutting process of friction material is performed in oil thus making it possible to prevent the temperature from rising due to cutting also the grinding stone and the work are relatively rotate in oil and load is given by means of oil pressure to enable the grinding stone and the work to be in contact thus preventing the temperature from rising due to cutting also in accordance with the present invention radially extended grooves are provided for the cutting surface of a grinding stone hence making it possible to exhaust chips externally and prevent the friction material and grinding store from being packed by chips in accordance with the present invention in a method for forming the frictional surface of a lockup clutch that produces the frictional surface by cutting process given to the friction material the cutting process is performed in such a manner that only the load of work 39 s own weight is given to the rotating grinding stone thus the process is executable without giving deformation to material and highly precise flatness of the surface is obtainable in accordance with the present invention the aforesaid additional cutting.