Let
X
X
be a connected, locally connected, normal
T
1
{T_1}
-space and let
M
M
be a closed connected, locally connected subspace of
X
X
. Suppose that
X
/
M
X/M
denotes the space obtained by identifying
M
M
in a single point, and that, for a connected space
Y
Y
,
ı
(
Y
)
\imath (Y)
denotes the multicoherence degree of
Y
Y
. In this paper, we prove that if
M
M
is unicoherent, then
ı
(
X
)
=
ı
(
X
/
M
)
\imath (X) = \imath (X/M)
. As an application of this result we prove that if
X
=
A
∪
B
X = A \cup B
, where
A
,
B
A,B
are closed subsets of
X
X
and
A
∩
B
A \cap B
is connected, locally connected and unicoherent, then
ı
(
X
)
=
ı
(
A
)
+
ı
(
B
)
\imath (X) = \imath (A) + \imath (B)
. Also, we prove that if
X
/
M
X/M
is unicoherent, then
ı
(
X
)
⩽
ı
(
M
)
\imath (X) \leqslant \imath (M)
.