  We show that all $2\otimes 4$ states with strong positive partial transposes
(SPPT) are separable. We also construct a family of $2\otimes 5$ entangled SPPT
states, so the conjecture on the separability of SPPT states are completely
settled. In addition, we clarify the relation between the set of all $2\otimes
d$ separable states and the set of all $2\otimes d$ SPPT states for the case of
$d=3,4$.
