We present a new approach based on the Davidson algorithm which provides eigenvalues and eigenvectors of selected highly excited (ro)vibrational states of polyatomic molecules. The key ingredient is a prediagonalization-perturbation scheme applied to a subspace of a curvilinear normal modes basis set (including diagonal anharmonicities). The efficiency of this method is illustrated by computing all vibrational states of the H2CO molecule, up to 9500 cm(-1) of internal excitation. Convergence of the levels can be assessed during the iteration process by looking at the residual \\((H) over cap $$ - E-alpha)\psi(alpha)>\\. (C) 2002 Published by Elsevier Science B.V.