We determine the composition series of the induced representation
$$\delta \left(\left[{\nu}^{b}\rho ,{\nu}^{c}\rho \right]\right)\times \delta \left(\left[{\nu}^{\frac{1}{2}}\rho ,{\nu}^{a}\rho \right]\right)\u22ca\sigma ,$$
where
$a,b,c\in \frac{1}{2}\left(2\mathbb{Z}+1\right)$
satisfy
$\frac{1}{2}\le a<b<c$,
$\rho $ is an
irreducible cuspidal unitary representation of a general linear group and
$\sigma $ is an
irreducible cuspidal representation of a classical group.
