Abstract: In allusion to the form solution to high order evolution equation, 4n-2 order evolution equation that is one of the best important standard type about time-delay distributed parameter system expand from two order evolution equation and construct the inner product to become 4n-2 dimension Halberd space at the same time. The generating operator of 4n-2 order evolution equation is obtained and it generates a semigroup when 4n-2 order evolution equation is changed into one order evolution equation set. The configuration form's semigroup is constructed and it's basic character is proved. In particular, the semigroup(n=1) intitules Golstein's.