Some of the essential tasks of a multiagent system (MAS) include distributed probabilistic reasoning, constraint reasoning, and decision making. Junction tree (JT) based agent organizations have been adopted by some MAS frameworks for their advantages of efficient communication and sound inference. In addition, JT organizations have the potential capacity to support a high degree of agent privacy. This potential, however, has not been fully realized. We present two necessary and sufficient conditions on the existence of JT organization given a MAS. Following these conditions, we propose a new algorithm suite, based on elimination in the so called boundary set of a MAS, that recognizes JT organization existence and constructs one if exists, while guaranteeing agent privacy on private variables, shared variables and agent identities.