Magnetic domain pattern and magnetic domain wall motion are particularly important to understand the magnetization process. Here, we investigated the magnetization process of perpendicularly exchange-biased Pt/Co/Au/Cr2O3/Pt stacked films based on observations of the magnetic domain. In particular, in contrast to previous studies which use fully exchange-biased state, we used the bi-exchange-biased state. We found that the magnetic domain pattern at the remanent state was robust against magnetic-field cycling, which is relevant to the absence of the training effect. The magnetization process was followed by domain wall propagation in the increasing branch of the magnetization curve. In the decreasing branch, both nucleation of the reversed domain and domain wall propagation were involved. The former was accompanied by latency, suggesting that thermal activation played a significant role in the nucleation of the reversed domain.