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We propose a new injection-locked optoelectronic oscillator (OEO) which is locked by a low frequency RF signal and without adding high speed devices. From a low frequency modulated optical carrier, the injection-locking effect in a Fabry-Pérot laser diode is able to generate and selectively amplify one high order harmonic component, which is subsequently injected into a single-loop OEO to lock one of the oscillation modes. This process can improve the injected signal quality and simultaneously implement a single-mode OEO with precise oscillation frequency. In the experiment demonstration, a 20-GHz single-mode OEO locked by a 1-GHz RF signal is obtained. The measured side-mode suppression ratio is 65 dB and the phase noise at 1-kHz frequency offset is -94.7 dBc/Hz.