  In a box of size $L$, a spatially antisymmetric square-well potential of a
purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an
initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of
which are all real for $g < g_c(l)$. The first partner potential is constructed
in closed form and discussed.
