Most existing relation extraction approaches exclusively target binary relations, and n-ary relation extraction is relatively unexplored. Current state-of-the-art n-ary relation extraction method is based on a supervised learning approach and, therefore, may suffer from the lack of sufficient relation labels. In this paper, we propose a novel approach to cross-sentence n-ary relation extraction based on universal schemas. To alleviate the sparsity problem and to leverage inherent decomposability of n-ary relations, we propose to learn relation representations of lower-arity facts that result from decomposing higher-arity facts. The proposed method computes a score of a new n-ary fact by aggregating scores of its decomposed lower-arity facts. We conduct experiments with datasets for ternary relation extraction and empirically show that our method improves the n-ary relation extraction performance compared to previous methods.