  Let G be a Frobenius group with the Frobenius kernel K. Suppose that G
contains a nontrival subgroup D \subseteq K such that the normalizer N_G(D)
\not\subseteq K. When D is no 2-group, Flavell proved, without using character
theory, that K is a subgroup of G. Based on this result, we further prove that
K is a subgroup when D is a 2-group.
