  We give new criteria for the irreducibility of parabolic induction on the
general linear group and its inner forms over a local non-archimedean field. In
particular, we give a necessary and sufficient condition when the inducing data
is of the form $\pi\otimes\sigma$ where $\pi$ is a ladder representation and
$\sigma$ is an arbitrary irreducible representation. As an application we
simplify the proof of the classification of the unitary dual.
