Unsupervised Bilingual Dictionary Induction methods based on the initialization and the self-learning have achieved great success in similar language pairs, e.g., English-Spanish. But they still fail and have an accuracy of 0% in many distant language pairs, e.g., English-Japanese. In this work, we show that this failure results from the gap between the actual initialization performance and the minimum initialization performance for the self-learning to succeed. We propose Iterative Dimension Reduction to bridge this gap. Our experiments show that this simple method does not hamper the performance of similar language pairs and achieves an accuracy of 13.64~55.53% between English and four distant languages, i.e., Chinese, Japanese, Vietnamese and Thai.