A new measurement of the circular polarization P y of the 1081-keV y line in 18 F has been performed. The result is ^(1081 keV) = (2.7 ± 5.7) x 10" 4 . This result, when averaged with those of recent measurements in 18 F, sets an upper constraint for the absolute value of the coupling constant/" of the weak TTNN interaction of |/J ^ 1.5 x 10~7.PACS numbers: 23.20.Lv, ll.30.Er, 21.30. + y, 27.20. + n Parity nonconservation in nuclei is understood as a consequence of the weak interaction among hadrons. In the low-energy limit one expects that nuclear parity-nonconservation effects can be estimated from a parity-nonconserving potential F pnc , to which there mainly contribute terms associated with the exchange of one virtual meson. 1 Among these the one arising from the exchange of one charged pion plays a peculiar role. In fact this term, which connects states with A T = 1, determines the long-range behavior of V pnc and is almost independent of the short-range part of the two-nucleon density matrix. Moreover, the value of the weak TTNN coupling constant f v comes out to be intimately related to the structure of the hadronic neutral weak currents and to the value of the quark masses.The measurement of the circular polarization P y of the 1081-keV y ray deexciting the first J n = 0~, T = 0 state in 18 F was recognized 2 as one of the most direct ways to determine the value of f^. This circular polarization is induced by the parity mixing of the state at 1081 keV with the one at 1042 keV (/^ = 0 + , r= 1).