Next basket recommendation (NBR) is the task of predicting the next set of items based on a sequence of already purchased baskets. It is a recommendation task that has been widely studied, especially in the context of grocery shopping. In next basket recommendation (NBR), it is useful to distinguish between repeat items, i.e., items that a user has consumed before, and explore items, i.e., items that a user has not consumed before. Most NBR work either ignores this distinction or focuses on repeat items. We formulate the next novel basket recommendation (NNBR) task, i.e., the task of recommending a basket that only consists of novel items, which is valuable for both real-world application and NBR evaluation. We evaluate how existing NBR methods perform on the NNBR task and find that, so far, limited progress has been made w.r.t. the NNBR task. To address the NNBR task, we propose a simple bi-directional transformer basket recommendation model (BTBR), which is focused on directly modeling item-to-item correlations within and across baskets instead of learning complex basket representations. To properly train BTBR, we propose and investigate several masking strategies and training objectives: (i) item-level random masking, (ii) item-level select masking, (iii) basket-level all masking, (iv) basket-level explore masking, and (v) joint masking. In addition, an item-basket swapping strategy is proposed to enrich the item interactions within the same baskets. We conduct extensive experiments on three open datasets with various characteristics. The results demonstrate the effectiveness of BTBR and our masking and swapping strategies for the NNBR task. BTBR with a properly selected masking and swapping strategy can substantially improve NNBR performance.