Firstly

this paper determines the period of ‘Interleaving’ sequences from de Bruijn sequences of

n

-stage and proves all 2

n

-tuple states are different from each other. Secondly

in the view of shift equivalence

the paper demonstrates that one can only construct two sequences from de Bruijn sequences of

n

-stage. For each one

the completion of its missing four 2

n

-tuple states can construct de Bruijn sequences of 2

n

-stage. Since there are two different ways to complete the missing bits

we can finally get four de Bruijn sequences of 2

n

-stage from one de Bruijn sequence of

n

-stage.