In the area of blockchain, numerous methods have been proposed for suppressing intentional forks by attackers more effectively than the random rule. However, all of them, except for the random rule, require major updates, rely on a trusted third party, or assume strong synchrony. Hence, it is challenging to apply these methods to existing systems such as Bitcoin. To address these issues, we propose another countermeasure that can be easily applied to existing proof of work blockchain systems. Our method is a tie-breaking rule that uses partial proof of work, which does not function as a block, as a time standard with finer granularity. By using the characteristic of partial proof of work, the proposed method enables miners to choose the last-generated block in a chain tie, which suppresses intentional forks by attackers. Only weak synchrony, which is already met by existing systems such as Bitcoin, is required for effective functioning. We evaluated the proposed method through a detailed analysis that is lacking in existing works. In networks that adopt our method, the proportion of the attacker hashrate necessary for selfish mining was approximately 0.31479 or higher, regardless of the block propagation capability of the attacker. Furthermore, we demonstrated through extended selfish mining that the impact of Match against pre-generated block, which is a concern in all last-generated rules, can be mitigated with appropriate parameter settings.