Pseudorandom sequence have been widly used in stream cipher

channel coding

and spread spectrum communication.m sequence is a excellent pseudorandom sequence.Based on m sequence

we first present reconstructing it’s state transition diagram and gained the state transition diagram of the new sequence called m subsequence in this paper.We prove that the first class m subsequences is existent

and present first class of m subsequences feedback functions.In the end we analyze m subsequences properties and affirm that possess with ideal balanced property、run property 、periodic property and good linear complexity.Statistic results show that m subsequences autocorrelation property have δ (t) function characteristic.More new m subsequence can be obtained by using this constructing method.