  We prove that the dual or any quotient of a separable reflexive Banach space
with the unconditional tree property has the unconditional tree property. Then
we prove that a separable reflexive Banach space with the unconditional tree
property embeds into a reflexive Banach space with an unconditional basis. This
solves several long standing open problems. In particular, it yields that a
quotient of a reflexive Banach space with an unconditional finite dimensional
decomposition embeds into a reflexive Banach space with an unconditional basis.
