The GMRES method is one of the most popular Krylov-subspace methods for solving nonsymmetric linear systems. The GMRES method shows a good convergence, but it has disadvantage of storage and computational costs. To remedy the disadvantage, restarted version of the GMRES method, the GMRES(m) method, is widely used as a practical choice. In this talk, we will analyze the unfixed update in GMRES(m) method based on the residual polynomials. Then a GMRES(m) method with Look-Back-type restart will be proposed in the framework of unfixed update. The numerical experiments indicate that the GMRES(m) method Look-Back-type restart is more efficient than the GMRES(m) method in many cases.