Based on the analysis of the existing ranking terminology or subject relevancy of documents methods through an intermediary collection as a catalyst (designated as Group B collection) for the purpose of non-interactive literature-based discovery, this article proposes a bi-directional document occurrence frequency based ranking method according to the “concurrence theory" and the degree and extent of the subject relevancy. This method explores and further refines the ranking method that is based on the occurrence frequency of the usage of certain terminologies and documents and injects a new insightful perspective of the concurrence of appropriate terminologies/documents in the “low occurrence frequency component” of three non-interactive document collections. A preliminary experiment was conducted to analyze and to test the significance and viability of our newly designed operational method.