An algorithm was derived to find candidate mappings between any two terminologies inside the UMLS, making use of synonymy, explicit mapping relations and hierarchical relationships among UMLS concepts. Using an existing set of mappings from SNOMED CT to ICD9CM as our gold standard, we managed to find candidate mappings for 86% of SNOMED CT terms, with recall of 42% and precision of 20%. Among the various methods used, mapping by UMLS synonymy was particularly accurate and could potentially be useful as a quality assurance tool in the creation of mapping sets or in the UMLS editing process. Other strengths and weaknesses of the algorithm are discussed.