In this paper, we determine the Cartier dual of certain finite group schemes of type
(p
n
, ..., p
n
), restricting ourselves to positive characteristic p case. They are given by
the kernel of certain endomormphisms of the fibre product W
l,A
×Spec A … ×Spec A
W
l,A
of the group scheme of Witt vectors of the length l. Moreover we can treat
the kernel of the endomorphism of a type F
n
+
a
1Fn-1 + … +
a
n
: W
l,A
→ W
l,A
as our special class, where F is the Frobenius endomorphism and
a
k
(k = 1, ..., n) are suitable Witt vectors.