  Continuous movement of discrete spectrum of the Schr\"{o}dinger operator
$H(z)=-\frac{d^2} {dx^2}+V_0+z V_1$, with $\int_0^\infty {x |V_j(x)| dx} <
\infty$, on the half-line is studied as $z$ moves along a continuous path in
the complex plane. The analysis provides information regarding the members of
the discrete spectrum of the non-selfadjoint operator that are evolved from the
discrete spectrum of the corresponding selfadjoint operator.
