In the course of preparing lectures on elementary quantum theory the author developed a way of presenting time-independent perturbation theory that seems to have some advantages over more familiar presentations. There is nothing fundamentally new in the method, and if any claim of greater power can be made for the new version, it is at best for situations in which high-order perturbations are of interest. Quantum-field theorists will no doubt recognize the relation of this presentation to much that has been done in their subject recently.