While previous works on privacy-preserving serial data publishing consider the scenario where sensitive values may persist over multiple data releases, we find that no previous work has sufficient protection provided for sensitive values that can change over time, which should be the more common case. In this work we propose to study the privacy guarantee for such transient sensitive values, which we call the global guarantee. We formally define the problem for achieving this guarantee and derive some theoretical properties for this problem. We show that the anonymized group sizes used in the data anonymization is a key factor in protecting individual privacy in serial publication. We propose two strategies for anonymization targeting at minimizing the average group size and the maximum group size. Finally, we conduct experiments on a medical dataset to show that our method is highly efficient and also produces published data of very high utility.