As a famous fully homomorphic encryption scheme that supports floating-point/real numbers, CKKS is widely applied in many real-world scenarios, such as privacy-preserving machine learning and data analysis. These applications demand high efficiency and fast implementation, making the variant scheme based on the residue number system (RNS) prevalent. In this paper, we present an exact modulus reduction algorithm for RNS-CKKS. Instead of using the fast basis conversion method, our algorithm employs iterative rescaling to achieve the desired result. Compared to the state-of-the-art, the algorithm originally proposed by Cheon et al. (SAC’18) and optimized by Halevi et al. (CT-RSA’19), our algorithm notably eliminates all floating-point computations. Furthermore, it reduces the number of modular multiplications and additions when \(\ell >(k^2-k-2)/2\) , thereby achieving better efficiency, where \(\ell \) is the level of ciphertexts and k is the number of auxiliary moduli. To demonstrate its practicability, we apply the proposed algorithm to CKKS bootstrapping. Experimental results show that our approach accelerates the modulus reduction algorithm in bootstrapping by a factor of \(15.2\%\sim 20.3\%\) for different ciphertext levels with a fixed \(k=5\) .