Distributional Semantic Models (DSMs) construct vector representations of word meanings based on their contexts. Typically, the contexts of a word are defined as its closest neighbours, but they can also be retrieved from its syntactic dependency relations. In this work, we propose a new dependency-based DSM. The novelty of our model lies in associating an independent meaning representation, a matrix, with each dependency-label. This allows it to capture specifics of the relations between words and contexts, leading to good performance on both intrinsic and extrinsic evaluation tasks. In addition to that, our model has an inherent ability to represent dependency chains as products of matrices which provides a straightforward way of handling further contexts of a word.