The Hierarchical Sub-Sentential Alignment (HSSA) method is a method to obtain aligned binary tree structures for two aligned sentences in translation correspondence. We propose to use the binary aligned tree structures delivered by this method as training data for preordering prior to machine translation. For that, we learn a Bracketing Transduction Grammar (BTG) from these binary aligned tree structures. In two oracle experiments in English to Japanese and Japanese to English translation, we show that it is theoretically possible to outperform a baseline system with a default distortion limit of 6, by about 2.5 and 5 BLEU points and, 7 and 10 RIBES points respectively, when preordering the source sentences using the learnt preordering model and using a distortion limit of 0. An attempt at learning a preordering model and its results are also reported.