  A nonstandard method for calculating the nuclear $2\nu\beta\beta$ - decay
amplitude is proposed. The method is based on the explicit use of those
approximate symmetries of a nuclear hamiltonian, which correspond to the
operators of allowed $\beta$ -- transitions. Within the framework of the
proposed method the mentioned amplitude is calculated for a wide range of
nuclei. The model parameters used in calculations are taken from independent
data. Calculated \bb half-lifes are compared with known experimental data.
