B polarization of cosmic background radiation from second-order scattering sources

B-mode polarization of the cosmic background radiation is induced from purely scalar primordial sources at second order in perturbations of the homogeneous, isotropic universe. We calculate the B-mode angular power spectrum C_l^{BB} sourced by the second-order scattering term in the full second-order Boltzmann equations for the polarized radiation phase-space density, which have recently become available. We find that at l\approx 200 the second-order effect is comparable to the first-order effect for a tensor-to-scalar ratio of r=10^{-6}, and to about 2\cdot 10^{-4} at l\approx 1000. It is always negligible relative to the weak-lensing induced contribution.