  We propose a new method for exact analytical calculation of the ground-state
energy of the Ising spin glass on strips. An outstanding advantage of this
method over the numerical transfer matrix technique is that the energy is
obtained for complex values of the probability describing quenched randomness.
We study the $\pm J$ and the site-random models using this method for strips of
various sizes up to $5\times\infty$. The ground-state energy of these models is
found to have singular points in the complex-probability plane, reminiscent of
Lee-Yang zeros in the complex-field plane for the Ising ferromagnet. The $\pm
J$ Ising model has a series of singularities which may approach a limiting
point around $p \sim 0.9$ on the real axis in the limit of infinite width.
