  Imposing twisted boundary conditions on the fermionic fields is a procedure
extensively used when evaluating, for example, form factors on the lattice.
Twisting is usually performed for one flavour and only in the valence, and this
causes a breaking of unitarity. In this work we explore the possibility of
restoring unitarity through the reweighting method. We first study some
properties of the approach at tree level and then we stochastically evaluate
ratios of fermionic determinants for different boundary conditions in order to
include them in the gauge averages, avoiding in this way the expensive
generation of new configurations for each choice of the twisting angle,
$\theta$. As expected the effect of reweighting is negligible in the case of
large volumes but it is important when the volumes are small and the twisting
angles are large. In particular we find a measurable effect for the plaquette
and the pion correlation function in the case of $\theta=\pi/2$ in a volume
$16\times 8^3$, and we observe a systematic upward shift in the pion dispersion
relation.
