We prove that
K
n
+
I, the complete graph of even order with a 1‐factor duplicated, admits a decomposition into 2‐factors, each a disjoint union of cycles of length
m
≥
5 if and only if
m
∣
n, except possibly when
m is odd and
n
=
4
m. In addition, we show that
K
n
+
I admits a decomposition into 2‐factors, each a disjoint union of cycles of lengths
m
1
,
…
,
m
t, whenever
m
1
,
…
,
m
t are all even.
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