This paper presents a new and low-cost approach for identifying sequentially untestable faults. Unlike the single fault theorem, where the stuck-at fault is injected only in the right-most time frame of the k-frame unrolled circuit, our approach can handle fault injection in any time frame within the unrolled sequential circuit. To efficiently apply our concept to untestable fault identification, powerful sequential implications are used to efficiently extend the unobservability propagation of gates in multiple time frames. Application of the proposed theorem to ISCAS?89 sequential benchmark circuits showed that more untestable faults could be identified using our approach, at practically no overhead in both memory and execution time.