Approximate nearest neighbour (ANN) search is one of the most important problems in computer science fields such as data mining or computer vision. In this paper, we focus on ANN for high-dimensional binary vectors and we propose a simple yet powerful search method that uses Random Binary Search Trees (RBST). We apply our method to a dataset of 1.25M binary local feature descriptors obtained from a real-life image-based localisation system provided by Google as a part of Project Tango. An extensive evaluation of our method against the state-of-the-art variations of Locality Sensitive Hashing (LSH), namely Uniform LSH and Multi-probe LSH, shows the superiority of our method in terms of retrieval precision with performance boost of over 20%