A
normalΓ‐magic rectangle set
M
R
S
Γ
(
a
,
b
;
c
) of order
a
b
c is a set of
c arrays of size
(
a
×
b
) whose entries are elements of a finite Abelian group
normalΓ of order
a
b
c, each appearing once, with all row sums in each rectangle equal to a constant
ω
∈
normalΓ and all column sums in each rectangle equal to a constant
δ
∈
normalΓ. There is known a complete characteristic of a
MRS
Γ
(
a
,
b
;
c
) for
{
a
,
b
}
≠
{
2
k
+
1
,
2
α
} for positive integers
k
,
α. The case
{
a
,
b
}
=
{
2
k
+
1
,
2
α
} is unsolved for
α
>
1. In this paper we show that a
MRS
Γ
(
2
k
+
1
,
4
;
4
l
+
2
) exists if and only if the group
normalΓ has more than one involution.
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