We show that the study of CP asymmetries in neutral B-meson decays provides a very sensitive probe of flavour-changing neutral currents (FCNC). We introduce two new angles, α SM and β SM, whose main feature is that they can be readily obtained from the measurement of the CP asymmetries a J/ ψK s , a π + π − and the ratio R u≡|V udV ub ∗|/|V cdV cb ∗| , providing a quantitative test of the presence of new physics in a model-independent way. Assuming that new physics is due to the presence of an isosinglet down-type quark, we indicate how to reconstruct the unitarity quadrangles and point out that the measurements of the above asymmetries, within the expected experimental errors, may detect FCNC effects, even for values of | ∑ i=1 3 V idV ib ∗/(V tdV tb ∗)| at the level of a few times 10 −2.