Relative time-stamping schemes prove the chronological sequence of digital documents and their integrity. Since the chronological sequence is verified by tracing the link between two timestamps, it is desirable that the length of the verification path is short. Buldas, Laud, Lipmaa, and Villemson have proposed the relative time-stamping scheme based on the binary link. In this paper, we extend the binary link to the ternary link, and apply it to the relative time-stamping scheme. We show that the maximum length of the verification path of the proposed scheme is shorter than that of the previous scheme. Moreover, we show that the average length of the proposed scheme is shorter than that of the previous scheme. Thus, the proposed time-stamping schemes is more efficient than the previous scheme.