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Unsupervised continual learning (UCL) of image representation has garnered attention due to practical need. However, recent UCL methods focus on mitigating the catastrophic forgetting with a replay buffer (i.e., rehearsal-based strategy), which needs much extra storage. To overcome this drawback, we propose a novel rememory-based SimSiam (RM-SimSiam) method to reduce the dependency on replay buffer. The core idea of RM-SimSiam is to store and remember the old knowledge with a data-free historical module instead of replay buffer.