  We report on an exact method for global fits of the CKM matrix by using the
necessary and sufficient conditions the data have to satisfy in order to find a
unitary matrix compatible with them, and this method can be applied to both
quark and lepton CKM matrices. The key condition writes $-1\le\cos\delta\le 1$
where $\delta$ is the phase that encodes the CP violation, and it is obtained
when one describes the CKM matrix in terms of four moduli of its entries. We
use it to reconstruct many approximate unitary matrices from the PDG data, and
by using the double stochasticity property of the unitary matrices we find a
strong dependence of $\sin 2\beta$ on $|U_{ub}|$, that implies also strong
correlations between $|U_{ij}|$ themselves, proving the constraining power of
this approach.
