A continuous observations near an small active region (AR) NOAA 10976 by the Solar Optical Telescope (SOT) and X-Ray Telescope (XRT) on board the Hinode satellite during Dec. 02 2007 from 15:50 UT to 19:59 UT. We observed that: (a) the filament formed by merging parallel fibrils into a twist structure. (b) the filament faded by reconnecting among its own loop structures, or being stripped into pieces.These process are always preceded by the brightening. (c) for the disappearance of the filament, it has close correlation with the activity, like untwisting or expanding, of its corresponding X-ray bright rope.