CLEFIA is a 128-bit block cipher proposed by Shirai et al. at FSE2007. It has been reported that CLEFIA has a 9-round saturation characteristic, in which 32bits of the output of 9-th round 112-th order differential equals to zero. By using this characteristic, a 14-round CLEFIA with 256-bit secret key is attacked with 2113 blocks of chosen plaintext and 2244.5 times of data encryption. In this paper, we focused on a higher order differential of CLEFIA. This paper introduces two new concepts for higher order differential which are control transform for the input and observation transform for the output. With these concepts, we found a new 6-round saturation characteristic, in which 24bits of the output of 6-th round 9-th order differential equals to zero. We also show a new 9-round saturation characteristic using 105-th order differential which is a 3-round extension of the 6-round one. If we use it, instead of 112-th order differential, using the meet-in-the-middle attack technique for higher order differential table, the data and computational complexity for the attack to 14-round CLEFIA can be reduced to around 2-5, 2-34 of the conventional attack, respectively.