We present a symmetry-adapted Lanczos method that uses projection operators to calculate energy levels with different symmetries from a single sequence of matrix-vector products. Compared with the conventional Lanczos method, this method has the advantage that energy levels are computed more efficiently and with symmetry labels. High-lying stretching energy levels of a coupled Morse oscillator Hamiltonian describing (SiH4)-Si-28 are calculated to demonstrate the advantage of the symmetry-adapted method. (C) 2001 American Institute of Physics.