The tasks of aspect identification and term extraction remain challenging in natural language processing. While supervised methods achieve high scores, it is hard to use them in real-world applications due to the lack of labelled datasets. Unsupervised approaches outperform these methods on several tasks, but it is still a challenge to extract both an aspect and a corresponding term, particularly in the multi-aspect setting. In this work, we present a novel unsupervised neural network with convolutional multi-attention mechanism, that allows extracting pairs (aspect, term) simultaneously, and demonstrate the effectiveness on the real-world dataset. We apply a special loss aimed to improve the quality of multi-aspect extraction. The experimental study demonstrates, what with this loss we increase the precision not only on this joint setting but also on aspect prediction only.