The optical second-harmonic generation (SHG) and the linear optical properties were investigated in a planar cell containing aligned nonchiral nematic derivative of B10H102-: 1-(4-heptyloxypyridin-1-yl)-10-(4-pentyl-1-thiacyclohexyl)-closo-decaborane (HPTD) as a function of temperature. The compound showed a low level of the SHG signal in the polycrystalline state, and no nonlinear optical effect was detected in the fluid nematic state (N) either in the presence or absence of an orienting electric field. When frozen, the resulting thermodynamically unstable nematic glassy phase (glassy N) unexpectedly exhibited the second-order nonlinear optical properties, implying a partial polar order in the arrangement of the in-plane-aligned molecules in a liquid-crystal cell. The efficiency of the SHG was analyzed for two polarization configurations yielding the main component of the second-order nonlinear susceptibility χxxx(2)=2.3±0.3 pm V-1 along the nematic director x. A comparison of the experimental susceptibility with a hypothetical one estimated from the vectorial component of the molecular hyperpolarizability showed a relatively low degree of the spontaneous polar order. The dispersion of the principal refractive indices in the glassy state of HPTD was derived from dichroic absorption spectra using an interference fringe method and fitted with a Sellmeier-type equation. At 527 nm the birefringence of HPTD is Δn=0.31.