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We propose a method for diagnosing single stuck-at faults under a built-in self-test (BIST) environment. Under the BIST environment, it is difficult to determine which BIST vectors produced errors due to the high degree of test response compaction. Therefore the detecting test set that is determined in BIST session includes non-detecting tests. We call the detecting test set determined after BIST session an "ambiguous diagnostic test set". Firstly, we propose a method for identifying candidate faults based on the ambiguous diagnostic test set. Moreover we propose a method for identifying candidate non-detecting tests that belong to the ambiguous diagnostic test set. Diagnosis by using more accurate diagnostic test sets is able to improve the diagnostic ambiguity.