This paper describes a very general approach to the calculation of the Zeeman splitting effect produced by an external magnetic field on the rotational levels of diatomic molecules. The method is valid for arbitrary values of the total electronic spin and of the magnetic field strength-that is, it holds for molecular electronic states of any multiplicity and for both the Zeeman and incomplete Paschen-Back regimes. It is based on an efficient numerical diagonalization of the effective Zeeman Hamiltonian, which can incorporate easily all the contributions one may eventually be interested in, such as the hyperfine interaction of the external magnetic field with the spin motions of the nuclei. The reliability of the method is demonstrated by comparing our results with previous ones obtained via formulae valid only for doublet states. We also present results for molecular transitions arising between nondoublet electronic states, illustrating that their Zeeman patterns show signatures produced by the Paschen-Back effect.