  Let $S$ be a $P^2$-knot which is the connected sum of a 2-knot with normal
Euler number 0 and an unknotted $P^2$-knot with normal Euler number $\pm2$ in a
closed 4-manifold $X$ with trisection $T_{X}$. Then, we show that the
trisection of $X$ obtained by the trivial gluing relative trisections of
$\overline{\nu(S)}$ and $X-\nu(S)$ is diffeomorphic to a stabilization of
$T_{X}$. It should be noted that this result is not obvious since
boundary-stabilizations introduced by Kim and Miller are used to construct a
relative trisection of $X-\nu(S)$. As a corollary, if $X=S^4$, the resulting
trisection is diffeomorphic to a stabilization of the genus 0 trisection of
$S^4$. This result is related to the conjecture that is a 4-dimensional
analogue of Waldhausen's theorem on Heegaard splittings.
