We present a new method adapted to the calculation of excited rovibrational states of semirigid molecules. It first relies on a description of the molecule in terms of polyspherical coordinates of Jacobi vectors, in order to obtain a compact expression for the kinetic energy operator (T) over cap (q). This general description is then adapted to the molecule considered by defining curvilinear normal modes from the corresponding zero order harmonic Hamiltonian (H) over cap (0)=(T) over cap (q(eq))+V-harm(q), the solutions of which are being used as the working basis set. The residual kinetic term DeltaT is treated mainly analytically in this basis, and displays no radial contribution. Anharmonic coupling DeltaV(q) is handled by means of a pseudospectral scheme based on Gauss Hermite quadratures. This method is particularly adapted to direct iterative approaches which only require the action of (H) over cap on a vector, without the need of the associated matrix, thus allowing ultralarge bases to be considered. An application to the excited vibrational states of the HFCO molecule is presented. It is shown in this example that energy levels can be trivially assigned from the leading expansion coefficient of the associated eigenvector. (C) 2001 American Institute of Physics.