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Models based on self-attention mechanisms have been successful in analyzing temporal data and have been widely used in the natural language domain. We propose a new model architecture for video face representation and recognition based on a self-attention mechanism. Our approach could be used for video with single and multiple identities. To the best of our knowledge, no one has explored the aggregation approaches that consider the video with multiple identities. The proposed approach utilizes existing models to get the face representation for each video frame, e.g., ArcFace and MobileFaceNet, and the aggregation module produces the aggregated face representation vector for video by taking into consideration the order of frames and their quality scores. We demonstrate empirical results on a public dataset for video face recognition called IJB-C to indicate that the self-attention aggregation network (SAAN) outperforms naive average pooling. Moreover, we introduce a new multi-identity video dataset based on the publicly available UMDFaces dataset and collected GIFs from Giphy. We show that SAAN is capable of producing a compact face representation for both single and multiple identities in a video. The dataset and source code will be publicly available.