  Recently Atobe-Oi-Yasuda established the newform theory for irreducible
tempered generic representations of unramified ${\rm U}_{2n+1}$ over
non-archimedean local fields. In this paper we extend their result to every
irreducible generic representations and compute the dimensions of the spaces of
oldforms. We also compute the Rankin-Selberg integrals attached to newforms and
oldforms under a natural assumption on the $\gamma$-factors defined by these
integrals.
