Let
Δ
′
{\Delta ’}
be the class of all derivatives, and let
[
Δ
′
]
[{\Delta ’}]
be the vector space generated by
Δ
′
{\Delta ’}
and O’Malley’s class
B
1
∗
B_1^{\ast }
. In [1] it is shown that every function in
[
Δ
′
]
[{\Delta ’}]
is of the form
g
′
+
h
k
′
{g’} + h{k’}
, where
g
,
h
g,h
, and
k
k
are differentiable, and that
f
∈
[
Δ
′
]
f \in [{\Delta ’}]
if and only if there is a sequence of derivatives
v
n
{v_n}
and closed sets
A
n
{A_n}
such that
∪
n
=
1
∞
A
n
=
R
\cup _{n = 1}^\infty {A_n} = {\mathbf {R}}
and
f
=
v
n
f = {v_n}
on
A
n
{A_n}
. The sequence of sets
A
n
{A_n}
together with the corresponding functions
v
n
{v_n}
is called a decomposition of
f
f
. In this paper we show that every Peano derivative belongs to
[
Δ
′
]
[{\Delta ’}]
. Also we show that for Peano derivatives the sets
A
n
{A_n}
can be chosen to be perfect.