  In the presence of the homogeneous electric field ${\bf E}$ and the
homogeneous perpendicular magnetic field ${\bf B}$, the classical trajectory of
a quantum particle on ${\mathbb R}^2$ moves with drift velocity $\alpha$ which
is perpendicular to the electric and magnetic fields. For such Hamiltonians the
absence of the embedded eigenvalues of perturbed Hamiltonian has been
conjectured. In this paper one proves this conjecture for the perturbations
$V(x, y)$ which have sufficiently small support in direction of drift velocity.
