A non-linear semantic mapping procedure is implemented for cross-language text matching at the sentence level. The method relies on a non-linear space reduction technique which is used for constructing semantic embeddings of multilingual sentence collections. In the proposed method, an independent embedding is constructed for each language in the multilingual collection and the similarities among the resulting semantic representations are used for cross-language matching. It is shown that the proposed method outperforms other conventional cross-language information retrieval methods.