Provided are a membrane and carrier head using the membrane for polishing apparatus. The membrane comprises a first fixing flap extending inwards from the upper part of a side portion, a second fixing flap extending upwards from the upper part of the side portion, wherein the second fixing flap has a first inclined part, a second inclined part and a third extending part of extending upwards whereby a compensation force generated by the inclined parts realize the constant pressing force to the edge of a substrate during a polishing process.