Unsupervised point cloud shape correspondence aims to establish point-wise correspondences between source and target point clouds. Existing methods obtain correspondences directly by computing point-wise feature similarity between point clouds. However, non-rigid objects possess strong deformability and unusual shapes, making it a longstanding challenge to directly establish correspondences between point clouds with unconventional shapes. To address this challenge, we propose an unsupervised Template-Assisted point cloud shape correspondence Network, termed TANet, including a template generation module and a template assistance module. The proposed TANet enjoys several merits. Firstly, the template generation module establishes a set of learnable templates with explicit structures. Secondly, we introduce a template assistance module that extensively leverages the generated templates to establish more accurate shape correspondences from multiple perspectives. Extensive experiments on four human and animal datasets demonstrate that TANet achieves favorable performance against state-of-the-art methods.