We study small magnetization oscillations around a saturated (spatially uniform) equilibrium state in a ferromagnetic particle of nanoscale dimension. It is shown that the normal magnetization oscillation modes are associated with the eigenfunctions of an appropriate self-adjoint operator which is directly related to the micromagnetic effective field. This formulation leads to a convenient scheme for the numerical computations of normal modes based on the diagonalization of an appropriate Hermitian matrix. In order to test the effectiveness of the method, the normal modes of a permalloy square thin-film are computed.