  We examine the contributions of odd-parity nuclear operators to the
two-neutrino double beta decay $0^+\rightarrow 0^+$ amplitude, which come from
the $P$-wave Coulomb corrections to the electron wave functions and the recoil
corrections to the nuclear currents. Although they are formally of higher order
in $\alpha Z/2$ or $v/c$ of the nucleon than the usual Fermi and Gamow-Teller
matrix elements, explicit calculations performed within the QRPA show that they
are significant when confronted with the experimental data.
