Recently a new public key cryptosystem based on a diagonal matrix has been proposed by Zheng. This system uses eigenvalues as a long-term key and random numbers as session key generators. However, there are a couple of flaws in that system. In this paper, we propose a new algorithm in which those flaws are all fixed. Our scheme is based on modular equations over a composite and uses a matrix of Jordan form. We also analyze the security of it.