The new approach for the fourth generation X-ray source-Multiturn Accelerator-Recuperator Source (MARS)-was proposed recently. The installation consists of the radiofrequency (RF) multiturn accelerator (similar to the race-track microtron) and long undulator(s). After passing through the undulator(s) the electron beam is decelerated in the same RF accelerating structure. Such energy recovery reduces dramatically the radiation hazard and decreases the required RF power. In this paper we present a more detail explanation of this scheme, and specify further the parameter limitations and requirements for the accelerator.