  Let F be a non-Archimedean local field. Consider G_n:= GL_n(F) and let M:=
G_l * G_{n-l} be a maximal Levi subgroup of G_n. In this article, we compute
the semisimplified Jacquet module of representations of G_n with respect to the
maximal Levi subgroup M, belonging to a particular category of representations.
Utilizing our results, we prove that the Jacquet module is multiplicity-free
for a specific subcategory of representations. Our findings are based on the
Zelevinsky classification.
