We show that new universality of Lyapunov spectra {lambda(i)} exists in Hamiltonian systems with many degrees of freedom. The universality appears in systems which are neither nearly integrable nor fully chaotic, and iris different from the one which is obtained in fully chaotic systems on one-dimensional chains as follows. One is that the universality is found in a finite range of large i/N rather than the whole range, where N is the number of degrees of freedom. Another is that Lyapunov spectra are not straight, while fully chaotic systems give straight Lyapunov spectra even on the three-dimensional simple cubic lattice. The universality appears when quadratic terms of a potential function dominate higher terms, harmonic motions are hence regarded as the base of global motions.