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Recently self-supervised learning has emerged as an effective approach to improve the performance of automatic speech recognition (ASR). Under such a framework, the neural network is usually pre-trained with massive unlabeled data and then fine-tuned with limited labeled data. However, the nonstreaming architecture like bidirectional transformer is usually adopted by the neural network to achieve competitive results, which can not be used in streaming scenarios. In this paper, we mainly focus on improving the performance of streaming transformer under the self-supervised learning framework. Specifically, we propose a novel two-stage training method during finetuning, which combines knowledge distilling and self-training. The proposed training method achieves 16.3% relative word error rate (WER) reduction on Librispeech noisy test set. Finally, by only using the 100h clean subset of Librispeech as the labeled data and the rest (860h) as the unlabeled data, our streaming transformer based model obtains competitive WERs 3.5/8.7 on Librispeech clean/noisy test sets.