Existing methods for out-of-distribution (OOD) detection use various techniques to produce a score, separate from classification, that determines how "OOD'' an input is. Our insight is that OOD detection can be simplified by using a neural network architecture which can effectively merge classification and OOD detection into a single step. Radial basis function networks (RBFNs) inherently link classification confidence and OOD detection; however, these networks have lost popularity due to the difficult of training them in a multi-layer fashion. In this work, we develop a multi-layer radial basis function network (MLRBFN) which can be easily trained. To ensure that these networks are also effective for OOD detection, we develop a novel depression mechanism. We apply MLRBFNs as standalone classifiers and as heads on top of pretrained feature extractors, and find that they are competitive with commonly used methods for OOD detection. Our MLRBFN architecture demonstrates a promising new direction for OOD detection methods.