  We apply the Painleve test for integrability to a new discrete
(differential-difference) nonlinear Schrodinger equation introduced by Leon and
Manna. Since the singular expansions of solutions of this equation turn out to
contain nondominant logarithmic terms, we conclude that the studied equation is
nonintegrable. This result supports the observation of Levi and Yamilov that
the Leon-Manna equation does not admit high-order generalized symmetries. As a
byproduct of the singularity analysis carried out, we obtain a new discrete
equation which should be integrable according to a conjecture of Weiss.
