Let
L
1
,
…
,
L
s
{\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s}
be
s
s
-distinct lines in
A
k
n
+
1
{\mathbf {A}}_k^{n + 1}
passing through the origin. Assume
s
=
(
n
n
+
d
)
−
λ
s = (_n^{n + d}) - \lambda
where
n
n
,
d
⩾
2
d \geqslant 2
. If
L
1
,
…
,
L
s
{\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s}
are in generic
s
s
-position, and
λ
=
0
\lambda = 0
.
1
,
…
,
n
−
1
1, \ldots ,n - 1
, then the Cohen-Macaulay type,
t
(
L
1
,
…
,
L
s
)
t({\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s})
, of
L
1
,
…
,
L
s
{\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s}
is given by the following formula:
t
(
L
1
,
…
,
L
s
)
=
(
n
−
1
n
+
d
−
1
)
−
λ
t({\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s}) = (_{n - 1}^{n + d - 1}) - \lambda
. This formula is known to be false for
λ
=
n
\lambda = n
. In this paper, we show that if
L
1
,
…
,
L
s
{\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s}
are in uniform position, and
λ
=
n
\lambda = n
. then
t
(
L
1
,
…
,
L
s
)
=
(
n
−
1
n
+
d
−
1
)
−
n
t({\mathfrak {L}_1}, \ldots ,{\mathfrak {L}_s}) = (_{\;n - 1}^{n + d - 1}) - n
.