A new method to calculate eigenfunctions and eigenvalues in a given energy range is proposed, which can therefore be applied to highly excited states of electronic and/or vibrational states of a molecule. The spectral components of a wave packet that lie outside the energy range are projected out through the time evolution; that is, the packet is screened onto the energy range. If the range includes only a single root, the corresponding eigenfunction is screened first, and the eigenvalue follows as its expectation value. For a case where there is more than a single root, several methods can be figured out. One typical and effective procedure is to construct local basis functions in terms of the aforementioned energy screened wave packets to represent the Hamiltonian in them and to diagonalize it. The concept to construct a local basis was originally developed by Neuhauser [J. Chem. Phys. 93, 2611 (1990)]. The present method performs it in a more efficient and theoretically satisfactory way.