It is a long outstanding conjecture that any (2

n

-1)-stage shuffle-exchange network (Omega network) is rearrageability for 2

emn×2

emn.Since then many researchers have attempted to solve this conjecture without success.A new result on the sufficiency proof has been established by Hasan.however

nobody have pointed out this proof to be incorrect.To clarify this fact is one of the objectives of this paper.The case

n

=3 was proved by many researchers.Using a constructive approach

this paper also proves that when

n

=4 the 7-stage 16×16 shuffle exchange network is rearrageability.The model of the balanced tree to avoid internal conflict

the repetition of permutations using connective graph and cycle grap

h

the concept of symmetry graph and equivalent transform are also presented in this paper.Based on the graph composition and bipartition the permutations 16×16 are divided into five classes

and total five assignment algorithms are proposed.These algorithms are more simple and clear and to be programmed.The techniques used for

n

=4 may provide useful hints for general case

n

＞4.