  The aim of this paper is to apply character properties of Frobenius group to
a local block form of an group algebra. We start by establishing a block form
of Brauer permutation Lemma by using block participation of conjugate classes
of a group $G$. Then we can define a pair of Frobenius corresponding blocks
between a group $G$ and its normal subgroup $N$. A near group condition is
given to determine a pair of Frobenius corresponding blocks. With a pair of
Frobenius corresponding blocks, we study its group structure. At last we prove
connections between nilpotent properties and Frobenius corresponding blocks.
