An exact equation for the angular momentum states of the diatomic molecule is derived. The eigenstates of the idealized Hund’s cases (a) and (b) are then calculated from the exact result. Example calculations of the matrix elements of the rotational Hamiltonian in the Hund’s case (a) basis are given and Hönl–London factors for (a)↔(a) and (b)↔(b) transitions are calculated. All calculations are carried out within the fully standard theory of angular momentum. Previous discussions of diatomic angular momentum states have invariably employed special methods such as consistently applied anomalies, and it is not generally known that such methods are unnecessary.