With the aim of increasing the numerical methods' precision regarding Maxwell's equations solving, a third order staggered FDTD method is proposed in this paper. The proposed method offers a trade-off between the accuracy and the stability, through the application of a third order staggered backward differentiation for the approximation of the temporal partial derivatives, and a fourth-order central difference approximation for the spatial derivatives approximation. The analysis of the numerical dispersion and the Courant-Friedrichs-Lewy condition demonstrates that the proposed method is more efficient than the traditional FDTD.