  We estimate the B-polarisation induced in the Cosmic Microwave Background by
the non-linear evolution of density perturbations. Using the second-order
Boltzmann code SONG, our analysis incorporates, for the first time, all
physical effects at recombination. We also include novel contributions from the
redshift part of the Boltzmann equation and from the bolometric definition of
the temperature in the presence of polarisation. The remaining line-of-sight
terms (lensing and time-delay) have previously been studied and must be
calculated non-perturbatively. The intrinsic B-mode polarisation is present
independent of the initial conditions and might contaminate the signal from
primordial gravitational waves. We find this contamination to be comparable to
a primordial tensor-to-scalar ratio of $r\simeq10^{-7}$ at the angular scale
$\ell\simeq100\,$, where the primordial signal peaks, and $r\simeq 5 \cdot
10^{-5}$ at $\ell\simeq700\,$, where the intrinsic signal peaks. Therefore, we
conclude that the intrinsic B-polarisation from second-order effects is not
likely to contaminate future searches of primordial gravitational waves.
