We investigated the instability of the moving rim in dewetting of slipping polymer films. Small fluctuations of the width of the rim get spontaneously amplified since narrower sections of the rim move faster than wider ones due to frictional forces being proportional to the width of the rim. Instability leads eventually to an autocontrol of the rim width by the continuous formation of droplets with a mean size proportional to the initial film thickness. Surprisingly, the mean dewetting velocity at late stages, averaged over the length of the rim, was found to be constant. Thus, the instability of the rim enabled a more efficient, i.e., faster, "drying" of the substrate. Nonslipping films did not show this instability.