In reality, a kind of allied m-sequence with finite series can be obtained by the way of state splicing. On the basis of this, we can prove the existence of this allied m-sequence when the series are any numbers by the way of mathematics: That is to separate the state of m-sequence shift register and the effective feedback bits based on the odd and even numbers, and study their influence on feedbacks respectively. On the basis of theory, we can get a finding that when series are any numbers, relative conjugate states have the condition to form an allied m-sequence. By analysis and tests, allied m-sequence, we get has a perfect pseudo random character.