This paper presents a novel method to improve the longitudinal coherence, efficiency and maximum photon energy of x-ray free electron lasers (XFELs). The method is equivalent to having two separate concatenated XFELs. The first uses one bunch of electrons to reach the saturation regime, generating a high power self-amplified spontaneous emission x-ray pulse at the fundamental and third harmonic. The x-ray pulse is filtered through an attenuator/monochromator and seeds a different electron bunch in the second FEL, using the fundamental and/or third harmonic as an input signal. In our method we combine the two XFELs operating with two bunches, separated by one or more rf cycles, in the same linear accelerator. We discuss the advantages and applications of the proposed system for present and future XFELs.