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Representing the spatial properties of facial attributes is a vital challenge for facial attribute recognition (FAR). Recent advances have achieved the reliable performances for FAR, benefiting from the description of spatial properties via extra prior information. However, the extra prior information might not be always available, resulting in the restricted application scenario of the prior-based methods. Meanwhile, the spatial ambiguity of facial attributes caused by inherent spatial diversities of facial parts is ignored. To address these issues, we propose a prior-free method for attribute spatial decomposition (ASD), mitigating the spatial ambiguity of facial attributes without any extra prior information. Specifically, assignment-embedding module (AEM) is proposed to enable the procedure of ASD, which consists of two operations: attribute-to-location assignment and location-to-attribute embedding. The attribute-to-location assignment first decomposes the feature map based on latent factors, assigning the magnitude of attribute components on each spatial location. Then, the assigned attribute components from all locations to represent the global-level attribute embeddings. Furthermore, correlation matrix minimization (CMM) is introduced to enlarge the discriminability of attribute embeddings. Experimental results demonstrate the superiority of ASD compared with state-of-the-art prior-based methods, while the reliable performance of ASD for the case of limited training data is further validated.