The system of Ax=b where A is an n*n real matrix which is nonsingular is derived from partial differential equations. The conjugate gradient methods (e.g. bi- conjugate gradient (Bi-CG), conjugate gradient squared (CGS) and Bi-CG stable (B--CGSTAB)) for solving larg nonsymetric linear system were explained in ([5],[7]). They are well-known that the methods suffers from to kinds of breakdowns. The first is due to the braekdown underling Lanczos process and the second is due to the fact that some iterates are not well defined be the Galerkin condition on the associate Krylov subspace .In this paper, we derive a simple modification of the Bi-CG, CGS, and Bi-CGSTAB algorithms, the composite step Bi-CG,CGS, and Bi-cgsta( SCBi-cg,CSCGS, CSBi-CGSTAB) algorithms, which is able to compute all the well-defined Bi-CG, CGS and Bi-CGSTAB iterates stably, assuming that the underlying Lanczos process dosnt breakdown.
