In this paper, we propose a test generation method for diagnosing transition faults. The proposed method assumes launch on capture test, and it generates test vectors for given fault pairs using a stuck-at ATPG tool so that they can be distinguished. If a given fault pair is indistinguishable, it is identified, and thus the proposed method achieves a complete diagnostic test generation. The conditions for distinguishing a fault pair are carefully considered, and they are transformed into the conditions of the detection of a stuck-at fault, and some additional logic gates are inserted in a CUT during the test generation process. Experimental results show that the proposed method can generate test vectors for distinguishing the fault pairs that are not distinguished by commercial tools, and also identify indistinguishable fault pairs.