In this paper, we present a test generation algorithm to improve scan chain failure diagnosis resolution. The proposed test generation algorithm creates a complete test set that guarantees each defective scan cell has unique failing behavior. This algorithm handles stuck-at fault and timing fault models. Problems and solutions that may happen in practical usage are discussed. We further extend the test generation algorithm to handle multiple failing scan chains and designs with embedded scan compression logic. Experimental results show the effectiveness of the proposed diagnostic test generation algorithm.