The agreement problem is usually exploited to improve the fault-tolerant capability of software systems. For self-organized networks like cloud computing architectures that possess highly decentralized and self-organized natures, consensus, which is essential to solving the agreement problem, in such networks cannot be achieved in the ways for traditional fixed networks. To address this problem of Consensus with Unknown Participants (CUP), a variant of the traditional consensus problem was proposed in the literature. Correspondingly, the CUP problem considering process crashes was also introduced, called the Fault-Tolerant Consensus with Unknown Participants (FT-CUP) problem. In this paper, we propose a new knowledge connectivity condition sufficient for solving the FT-CUP problem. Our new condition is weaker and more viable than an existing one, which is hard to implement in practice.