The relativistic magnetron is the most compact and efficient high-power microwave source. In order to further increase the total efficiency of microwave generation in a relativistic magnetron with diffraction output with a low-energy state of electrons that is formed between two virtual cathodes (VCs) in the interaction space, the second VC at the downstream end of the interaction space is replaced with a magnetic mirror that reflects all leakage electrons back into the interaction space. Previously these leakage electrons were deposited on the anode surface without interacting with the microwaves. Particle-in-cell simulations show that this configuration of relativistic magnetron increases the electronic efficiency from 86% to 92%, and increases the total efficiency up to the maximal electronic efficiency. This is a record high efficiency of microwave generation in a relativistic magnetron or any other gigawatt-class, gigahertz-frequency HPM source.