Attributed network embedding has received much interest from the research community as most of the networks come with some content in each node, which is also known as node attributes. Existing attributed network approaches work well when the network is consistent in structure and attributes, and nodes behave as expected. But real world networks often have anomalous nodes. Typically these outliers, being relatively unexplainable, affect the embeddings of other nodes in the network. Thus all the downstream network mining tasks fail miserably in the presence of such outliers. Hence an integrated approach to detect anomalies and reduce their overall effect on the network embedding is required. Towards this end, we propose an unsupervised outlier aware network embedding algorithm (ONE) for attributed networks, which minimizes the effect of the outlier nodes, and hence generates robust network embeddings. We align and jointly optimize the loss functions coming from structure and attributes of the network. To the best of our knowledge, this is the first generic network embedding approach which incorporates the effect of outliers for an attributed network without any supervision. We experimented on publicly available real networks and manually planted different types of outliers to check the performance of the proposed algorithm. Results demonstrate the superiority of our approach to detect the network outliers compared to the state-of-the-art approaches. We also consider different downstream machine learning applications on networks to show the efficiency of ONE as a generic network embedding technique. The source code is made available at https://github.com/sambaranban/ONE.