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Self-supervised learning (SSL), which utilizes the input data itself for representation learning, has achieved state-of-the-art results for various downstream speech tasks. However, most of the previous studies focused on offline single-talker applications, with limited investigations in multi-talker cases, especially for streaming scenarios. In this paper, we investigate SSL for streaming multi-talker speech recognition, which generates transcriptions of overlapping speakers in a streaming fashion. We first observe that conventional SSL techniques do not work well on this task due to the poor representation of overlapping speech. We then propose a novel SSL training objective, referred to as bi-label masked speech prediction, which explicitly preserves representations of all speakers in overlapping speech. We investigate various aspects of the proposed system including data configuration and quantizer selection. The proposed SSL setup achieves substantially better word error rates on the LibriSpeechMix dataset.