J.Zhuo Appl.Muth.Comput.92 (1998;49 58 53 it is easy to give the solution procedure of the linear system (1).Here we des- cribe the following. Algorithm 1. 1.Given 4=[d E R*",B=b,ER"and C=Ci E R"satisfying Con- dition I and given f∈Rm,g∈R”. 2.L==chol(A)or using expression (7). 3.Computing L8 =[g from LaL=B or using expression (8). 4.L =[v]chol(C+LgL)or using expression (9). 5.Computing from ,2)0)() 6.Obtained the final solution of the linear system (1)from (日))-) As a special case,if we have C=0 in the linear system (1).i.e.. -(8) then we can obtain the analogous factorization form. Using matrices La and La obtained in Theorem I,and Lg full row rank.we have the Cholesky factorization of LaL.i.e.. L,LX=LBL牙 where LER"*"is low triangular.Hence the following theorem is proved Theorem 2.Let A G- B B O and matrices A and B sutisfy Condition I.then there always exists a factorizution G:=L2Lg, (10) where