Unsupervised neural machine translation (UNMT) models are trained with pseudo-parallel sentences constructed by on-the-fly back-translation using monolingual corpora. However, the quality of pseudo-parallel sentences cannot be guaranteed, which hinders the final performance of UNMT. This paper demonstrates that although UNMT usually generates mistakes during pseudo-parallel data construction, some of them can be corrected by the token-level translations that exist in the embedding table. Therefore, we propose a self-correction method to automatically improve the quality of pseudo-parallel sentences during training, thereby enhancing translation performance. Specifically, for a pseudo sentence pair, our self-correction method first estimates the alignment relations between tokens by treating and solving it as an optimal transport problem. Then, we measure the translation reliability for each token and detect the mis-translated ones. Finally, the mis-translated tokens are corrected with real-time computed token-by-token translations based on the embedding table, yielding a better training example. Considering that the modified examples are semantically equivalent to the original ones when UNMT converges, we introduce second-phase training to strengthen the output consistency between them, further improving the generalization capability and translation performance. Empirical results on widely used UNMT datasets demonstrate the effectiveness of our method and it significantly outperforms several strong baselines.