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We have developed a new control method for the Quasi- Zenith Satellite (QZS) remote synchronization system for an onboard crystal oscillator (RESSOX). The new method utilizes both L1 and L2 positioning signals of the QZS. We also found that precise orbit information and the estimation of delays, such as those caused by the ionosphere and troposphere, are not necessary to realize the RESSOX technology. The estimation of the delays of the L1-, L2- and Ku-band signals caused by the ionosphere and other sources can be calculated separately during feedback control, and the results of Ku-band delay are used to generate the RESSOX control signal. The simulation results showed that synchronization of within 3 ns between the ground site clock and the QZS site clock is achievable. Experimental results on the ground also confirmed that synchronization within 3 ns is feasible.