We present an approach to reduce the numerical dispersion of the FDTD method for its conditionally and unconditionally stable implementations. Significant reduction of the numerical error is achieved in a wide frequency band and for low spatial sampling rates. The cancellation of the numerical dispersion errors is achieved by the proposed combination of second order and higher order finite-difference approximations for the spatial derivatives of Maxwellpsilas equations. Also, the proposed update schemes are more accurate and faster than the corresponding higher order FDTD schemes for the same time-space discretization. Finally, test examples are provided for validation and verification purposes.