Based on single-beam polarization second-harmonic generation, when polarizations of both initial input beam and second- harmonic output beam are linearly polarized in chiral experimental setup, uniqueness of nonzero experimental fitting expansion coefficients f，g and h related to p + s- polarized second- harmonic signal is reported. The results indicate that for organic optical molecules with D- p- A structured, these experimental expansion coefficients are unique for s- and p±s-polarized initial beams, but they are not unique for p- polarized initial beam, and the simulated results of the p + s- polarized second- harmonic signal can completely explain the contradiction between theory and experiment. To precisely characterize all the secondorder nonlinear susceptibility tensor components of the D- p- A structured materials, it is necessary to avoid using the p-polarized initial beam in a chiral experimental setup.