In laser-pointing-related applications, when only the centroid of a laser spot is considered, then the position and angular errors of the laser beam are often coupled together. In this study, the decoupling of the position and angular errors is achieved from one single spot image by utilizing a neural network technique. In particular, the successful application of the neural network technique relies on novel experimental procedures, including using an appropriate small-focal-length lens and tilting the detector, to physically enlarge the contrast of different spots. This technique, with the corresponding new system design, may prove to be instructive in the future design of laser-pointing-related systems.