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The attention mechanism has become the \emph{de facto} module in scene text recognition (STR) methods, due to its capability of extracting character-level representations. These methods can be summarized into implicit attention based and supervised attention based, depended on how the attention is computed, i.e., implicit attention and supervised attention are learned from sequence-level text annotations and or character-level bounding box annotations, respectively. Implicit attention, as it may extract coarse or even incorrect spatial regions as character attention, is prone to suffering from an alignment-drifted issue. Supervised attention can alleviate the above issue, but it is character category-specific, which requires extra laborious character-level bounding box annotations and would be memory-intensive when handling languages with larger character categories. To address the aforementioned issues, we propose a novel attention mechanism for STR, self-supervised implicit glyph attention (SIGA). SIGA delineates the glyph structures of text images by jointly self-supervised text segmentation and implicit attention alignment, which serve as the supervision to improve attention correctness without extra character-level annotations. Experimental results demonstrate that SIGA performs consistently and significantly better than previous attention-based STR methods, in terms of both attention correctness and final recognition performance on publicly available context benchmarks and our contributed contextless benchmarks.