To build a common controlled vocabulary is a formidable challenge in medical informatics. Due to vast scale and multiplicity in interpretation of medical data, it is natural to face overlapping terminologies in the process of practicing medical informatics [A. Rector, Clinical terminology: why is it so hard? Methods Inf. Med. 38 (1999) 239-252]. A major concern lies in the integration of seemingly overlapping terminologies in the medical domain and this issue has not been well addressed. In this paper, we describe a novel approach for medical ontology integration that relies on the theory of Algorithmic Semantic Refinement we previously developed. Our approach simplifies the task of matching pairs of corresponding concepts derived from a pair of ontologies, which is vital to terminology mapping. A formal theory and algorithm for our approach have been devised and the application of this method to two medical terminologies has been developed. The result of our work is an integrated medical terminology and a methodology and implementation ready to use for other ontology integration tasks.