We have carried out a quantum mechanical calculation of the differential conductance of the double-bend channels defined by abrupt changes in geometry. The constriction has been connected to two semi-infinite two-dimensional electron gas regions, which serve as emitter and collector when a source - drain voltage is applied. We assume that the source - drain voltage has a symmetric drop along the double-bend quantum channel, and that the main drop occurs at the boundaries where the backscattering takes place. Our results show that the source - drain voltage strongly smears the resonant peaks in the differential conductance corresponding to the resonant tunnelling via the quasibound states below the first conductance plateau of the double-bend quantum channel. Our calculations also show that additional conductance quasiplateaus develop as the source - drain voltage is increased, and that the edges of the voltage-induced conductance quasiplateaus are shifted linearly with the applied source - drain voltage.