This papr discusses algorithm and convergence of twostage iteratve procedure for solving systems of symmetric positive definite linear equation Ax=b. On the basis of nature splitting of A, this algorithm makes two-step linear iterative procedure (named outer iteration) and makes convergent inner iteraton of any kind.They generate a sequence of approximations {x_h} w.hich converges to the solution Ax=b quickly. This paper also proves is convergene and gives the estimation of error.