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Automatic segmentation of skin lesions is still challenging due to ambiguous boundary and noise interference of lesion regions. Recent exiting Transformer based methods often directly apply Transformer to obtain long-range dependency to overcome these problems. However, they generally do not consider that patch partitioning strategy of Transformer could lead to the loss of local details around boundaries. Furthermore, dependencies across local windows only represent global information at a coarse level. Therefore, to overcome the limitations, two novel modules, Local Focus Module (LFM) and Global Augmentation Module (GAM) are proposed in this paper. LFM learns the local context around boundary regions to strengthen the discrimination between classes. And GAM learns the global context at a finer level to enhance global feature representation. Integrating LFM and GAM, a new Transformer encoder based framework, Local-Global Augmentation Network (LGANet), is proposed. LGANet is efficient in segmenting lesions with ambiguous boundary and with noise interference and its performances are demonstrated with extensive experiments on two public skin lesion segmentation datasets.