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We propose and demonstrate a novel configuration for depolarized interferometric fiber-optic gyroscopes (IFOGs). This configuration utilizes optical compensation between two orthogonal polarizations for suppressing errors induced by polarization nonreciprocity. Theoretical analysis shows that it is a new approach different from conventional IFOGs where a polarizer is mandatory. An experimental demonstration of the proposed IFOG (2097-m coil, open-loop configuration) achieves a low bias drift of 0.016 °/h in detecting the Earth's rotation rate. Furthermore, this configuration requires no polarizer or any other polarization-maintaining device.