The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function
σ
r
♯
(
n
;
N
/
4
,
N
)
{\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N)
in as a simple form as possible, where
N
/
4
N\hspace{-0.08em}\text{/}\hspace{-0.08em}4
is an arbitrary odd positive integer. This generalizes previous result in combination with Cho and Kim, which is about the case
N
=
4
N=4
. While obtaining our main theorem, we derive some generalizations of other identities to the case that we are dealing with.