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Lifelong or continual learning remains to be a challenge for artificial neural network, as it is required to be both stable for preservation of old knowledge and plastic for acquisition of new knowledge. It is common to see previous experience get overwritten, which leads to the well-known issue of catastrophic forgetting, especially in the scenario of class-incremental learning (Class-IL). Recently, many lifelong learning methods have been proposed to avoid catastrophic forgetting. However, models which learn without replay of the input data, would encounter another problem which has been ignored, and we refer to it as prior information loss (PIL). In training procedure of Class-IL, as the model has no knowledge about following tasks, it would only extract features necessary for tasks learned so far, whose information is insufficient for joint classification. In this paper, our empirical results on several image datasets show that PIL limits the performance of current state-of-the-art method for Class-IL, the orthogonal weights modification (OWM) algorithm. Furthermore, we propose to combine self-supervised learning, which can provide effective representations without requiring labels, with Class-IL to partly get around this problem. Experiments show superiority of proposed method to OWM, as well as other strong baselines.