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Reducing the transverse relaxation rate of alkali atoms is crucial to improve the sensitivity of the magnetometers. In a perturbative treatment of the effects of the magnetic-field gradients, the transverse relaxation rates of alkali atoms are predicted to be proportional to the square of the longitudinal magnetic-field gradient. The theoretical predictions are confirmed in our experiments. The magnetic-field gradients in the vapor cell are measured by experiments. The magnetic-field gradient in the cell is suppressed drastically through compensating it with the compensation coils. Experimental results show that suppressing the magnetic-field gradient can reduce the transverse relaxation rate of alkali atoms significantly. This study contributes to the development of ultra-high sensitivity alkali atomic magnetometers.