  In this article, we study the full theta lifting for two cases of type II
reductive dual pairs over a nonarchimedean local field. Firstly, we determine
the structure of the full theta lifts of all irreducible representations for
dual pair $(\mathrm{GL}(2),\mathrm{GL}(2))$. Secondly, we prove that the full
theta lift of an irreducible tempered representation is irreducible and
tempered for dual pair $(\mathrm{GL}(n),\mathrm{GL}(n+1))$, where $n$ is a
positive integer.
