A scheme of electron radiation output is proposed to solve the problem of overheating of the optical resonator mirrors in free-electron lasers (FEL) with high average radiation power. Such a structure acts on the electron beam, which is initially grouped in the first section of the undulator due to interaction with the mode of the optical resonator. In subsequent sections, it rotates at a small angle relative to the optical axis while maintaining its grouping, and its coherent radiation goes beyond the limits of the resonator mode. The electron outcoupling system is installed on the last of the three lasers of the Novosibirsk FEL. It consists of three undulators, two quadrupoles, and dipole correctors located between them. There are thus two possible configurations, as the electron beam can be rotated in both the second and third undulator. Preliminary estimates of the radiation power are considered. Different configurations of the electron radiation output system of the Novosibirsk FEL are compared.