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We propose a block-online algorithm of guided source separation (GSS). GSS is a speech separation method that uses diarization information to update parameters of the generative model of observation signals. Previous studies have shown that GSS performs well in multi-talker scenarios. However, it requires a large amount of calculation time, which is an obstacle to the deployment of online applications. It is also a problem that the offline GSS is an utterance-wise algorithm so that it produces latency according to the length of the utterance. With the proposed algorithm, block-wise input samples and corresponding time annotations are concatenated with those in the preceding context and used to update the parameters. Using the context enables the algorithm to estimate time-frequency masks accurately only from one iteration of optimization for each block, and its latency does not depend on the utterance length but predetermined block length. It also reduces calculation cost by updating only the parameters of active speakers in each block and its context. Evaluation on the CHiME-6 corpus and a meeting corpus showed that the proposed algorithm achieved almost the same performance as the conventional offline GSS algorithm but with 32x faster calculation, which is sufficient for real-time applications.