The nonlinear normal mode of a 2 DOF piecewise linear system was investigated. First, the initial conditions of the in phase and the anti phase nonlinear normal mode motions as well as their curves in configuration space were studied theoretically, and the modal frequencies were obtained by weighted average method. Then, numerical method was adopted in order to determine the curves of nonlinear normal modes in the configuration space and the corresponding modal frequencies. The comparison between the theoretical and the numerical results shows that the proposal formulae of modal frequencies in this paper are more accurate than the one proposed previously in the literature. It is demonstrated that the system may own the so called superabundant modes beside the in phase and the anti phase modes, namely, the number of modes may exceed the number of the degree of freedom of the system. The appearance of the superabundant modes indicates the internal resonance between the in phase and the anti phase modes.