The relativistic magnetron is one of the most attractive high-power microwave sources, due to its compactness with high efficiency. It can generate hundreds of megawatts of microwave power in the L- and S-bands. However, the efficiency of the magnetron is often limited due to the mode stability. In this Letter, three-dimensional particle-in-cell simulation suggests even further increase of total efficiency of the magnetron can be realised via mode stabilisation using a self-excited extended interaction in a collector region. A six-vaned radial relativistic magnetron with a single radial output port powered by 400 kV, <10 kA electron beam with a 70 ns pulse demonstrates >900 MW with an efficiency of ∼48%. This improvement is attributed to the mode locking of operating π-mode by a power-boosted TE315 mode excited in the extended cavity.