An effective method for suppressing intentional forks in a blockchain is the last-generated rule, which selects the most recent chain as the main chain in the event of a chain tie. This rule helps invalidate blocks that are withheld by adversaries for a certain period. However, existing last-generated rules face an issue in that their application to the system is not fully localized. In conservative cryptocurrency systems such as Bitcoin, it is desirable for methods to be applied in a fully local manner. In this paper, we propose a locally applicable last-generated rule. Our method is straightforward and is based on a relative time reference. By conservatively setting the upper bound on the clock skew ΔOito 54 s, we show through simulation experiments that our proposed method reduces the proportion γ of honest miners following the adversary during chain ties by more than 76% in Bitcoin compared to the existing local method, i.e., the random rule.