Abstract: Recently unsupervised Bilingual Lexicon Induction(BLI) without any parallel corpus has attracted much research interest. One of the crucial parts in methods for the BLI task is the matching procedure. Previous works impose a too strong constraint on the matching and lead to many counterintuitive translation pairings. Thus We propose a relaxed matching procedure to find a more precise matching between two languages. We also find that aligning source and target language embedding space bidirectionally will bring significant improvement. We follow the previous iterative framework to conduct experiments. Results on standard benchmark demonstrate the effectiveness of our proposed method, which substantially outperforms previous unsupervised methods.