Weak neutral currents give a significant contribution to parity violation in nuclear transitions. Many calculations have been presented on this effect. These depend strongly on the evaluation of the strength of the weak nucleon-pion coupling, on the treatment of the nuclear wave functions and on the choice of models of the weak neutral currents and others. In this note first we present an estimation of the weak nucleon-pion coupling constant and comment on previous evaluation of this quantity. Secondly, taking into account the modified factorization approach proposed by Donoghue and adopting previous evaluation of nuclear matrix elements in the literature, we calculate the parity violating quantities in various transitions. The recently claimed discrepancy between a theoretical prediction and an experimental result of the Pasadena-Los Angeles-Seattle group on the circular polarization of γ rays in the transitions of 18F disappears in our treatment.