Abstract The Burrows–Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT is a bijective variant of it that has not yet been studied for text indexing applications. We fill this gap by proposing a self-index built on the bijective BWT. The self-index applies the backward search technique of the FM-index to find a pattern P with O (| P| lg⁡| P|) backward search steps. Additionally, we propose the first linear-time construction algorithm that is based on SAIS, improving the best known result of O (n lg⁡ n/lg⁡ lg⁡ n) time to linear.