The computation using Chinese Remainder Theorem in RSA cryptosystem is well suited in the digital signature or decryption processing due to its low computational load compared to the case of general RSA without CRT. Since the RSA-CRT algorithm is vulnerable to many fault insertion attacks, some countermeasures against them were proposed. Among several countermeasures, Yen et al. proposed two schemes based on fault propagation method. Unfortunately, a new vulnerability was founded in FDTC 2006 conference. To improve the original schemes, Kim et al. recently proposed a new countermeasure in which they adopt the AND operation for fault propagation. In this paper, we show that the proposed scheme using AND operation without checking procedure is also vulnerable to fault insertion attack with chosen messages.