To provide a lock-up clutch used in a torque converter and capable of improving heat resistance of an outside diameter side friction member for performing slip control.

This drawing is an enlarged cross sectional view of main parts of parts of a front cover 21 and a clutch piston 5 of the lock-up clutch for the torque converter. The friction member is divided into an outside diameter side friction member 71 for performing slip control for making μ-ν characteristic a positive gradient and an inside diameter side friction member 72 having large coefficient of static friction and large torque capacity when engaging the clutch. In this invention, the outside diameter side friction member is further divided into an outer periphery side friction member 71A and an inner periphery side friction member 71B, and each of them is stuck to either of the front cover 21 and the clutch piston 5. Consequently, large quantity of heat generated at slip control time is dispersed onto a front cover 21 side having large heat capacity and high heat radiation effect and a piston 5 side and escapes, thereby increasing heat resistance of the outside diameter side friction member 71.