  We consider the magnetic Schr\"odinger operator $H=(i \nabla +A)^2- V$ with a
non-negative potential $V$ supported over a strip which is a local deformation
of a straight one, and the magnetic field $B:=\mathrm{rot}(A)$ is assumed to be
nonzero and local. We show that the magnetic field does not change the
essential spectrum of this system, and investigate a sufficient condition for
the discrete spectrum of $H$ to be empty.
