  We have extended the formalism for the two-neutrino double beta decay by
including the weak-magnetism term, as well as other second-forbidden
corrections. The weak magnetism diminishes the calculated half-lives in $\sim
10%$, independently of the nuclear structure. Numerical computations were
performed within the pn-QRPA, for $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$
and $^{130}Te$ nuclei. No one of the second-forbidden corrections modifies
significantly the spectrum shapes. The total reduction in the calculated half
lives varies from 6% up to 32%, and strongly depend on the nuclear interaction
in the particle-particle $S=1,T=0$ channel. We conclude that the higher order
effects in the weak Hamiltonian would hardly be observed in the two-neutrino
double beta experiments.
