Reducing the influence of electrical crosstalk is crucial for the development of fiber optic gyroscopes. We present a six-state modulation method that takes advantage of highly flexible modulation voltages to eliminate the correlation between the modulation voltage with a fixed phase delay and the demodulation sequence. Theoretical analysis indicates that our approach can eliminate the impact of crosstalk with a fixed phase delay at any modulation depth. Experimental measurements demonstrate that compared to the conventional four-state modulation method, the zero bias is reduced by about 0.3319°/h at the modulation depth of π/2 when our method is applied. Additionally, at the depths of π/2, 2π/3, and 7π/8, the bias instability is reduced by approximately 30%, and the angular random walk (ARW) is reduced by over 60%. The results confirm its effectiveness in decreasing electrical crosstalk, which holds profound implications for enhancing the accuracy of fiber optic gyroscopes.