Workflow management technology has become a key means to improve enterprise productivity. More and more workflow systems are crossing organizational boundaries and may involve multiple interacting organizations. This article focuses on a type of loosely coupled workflow architecture with collaborative tasks, i.e., each business partner owns its private business process and is able to operate independently, and all involved organizations need to be synchronized at a certain point to complete certain public tasks. Because of each organization's privacy consideration, they are unwilling to share the business details with others. In this way, traditional correctness verification approaches via reachability analysis are not practical as a global business process model is unavailable for privacy preservation. To ensure its globally correct execution, this work establishes a correctness verification approach for the cross-organizational workflow with task synchronization patterns. Its core idea is to use local correctness of each suborganizational workflow process to guarantee its global correctness. We prove that the proposed approach can be used to investigate the behavioral property preservation when synthesizing suborganizational workflows via collaborative tasks. A medical diagnosis running case is used to illustrate the applicability of the proposed approaches.