Reward prediction error (RPE), which refers to the difference between received reward and expected reward, has been proposed as the key driving force for learning from both animal learning theories and from reinforcement learning models. While the discovery of RPE neural correlates in midbrain dopamine (DA) neurons has been highly influential, extensive preliminary data from my lab support the existence of a similar RPE signal in another major neuromodulatory system in the basal forebrain (BF), particularly among a special group of noncholinergic neurons which we refer to as BF bursting neurons. In this talk, I will describe how we use the BF RPE signal to gain insights on the decision making process during new associative learning. By tracking the temporal evolution of this BF RPE signal during new learning, we observe that the BF RPE signal temporally backpropagates from the time of reward to the reward-predicting stimulus in discrete steps. The dynamics of BF RPE backpropagation reveals how animals establish their internal reward prediction models during the early phase of new learning, and how such models undergo stepwise expansion to incorporate new reward predictors. These results will also add to the functional significance of the poorly understood noncholinergic BF neurons, which have been recently demonstrated to play key roles in top-down attention and reward-based decision making.