Abstract: In order to study structure of the generalized stochastic matrices algebra SL,in[1],the author defined the subalgebra W（V₁，V₂，…，V_m）concerning directions of vectors V₁，V₂，…，V_m.  §1   of  this   paper,we   study   structure   of W（V₁，V₂，…，V_m). And   in §2,we   research doubly stability subalgebra concerning directions of vectors,and prove a structure theorem of it. Final,we get:The generalized doubly stochastic matrices algebra is a semi-simple algebra.

Key words: stability subalgebra concerning directions of vectors, doubly stability subalgebra concerning direction of vectors, doubly stochastic matrices algebra, semi-simple algebra