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 \simeq 10 ^ { -7 } at the angular scale \ell \simeq 100 , where the primordial signal peaks , and r \simeq { 5 } \times 10 ^ { -5 } at \ell \simeq 700 , 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 .