To detect the critical nodes that can lead to topology partition in a Mobile Ad Hoc Network (MANET), a Cross-link-tolerant Partition Detection Algorithm (CPDA) was proposed. Through utilizing the information of adjacent nodes, CPDA could eliminate the cross-links' impact on the elementary loop. Therefore, it solved the problem that the existing algorithm of Distributed Partition Detection Protocol (DPDP) based on elementary-loop could not address cross links, which improved the accuracy of detection of critical nodes. The performance results show that CPDA has no limitation on network topology and outperforms DPDP in terms of detection accuracy and overhead.