We introduce a new simple implementation of a numerical scheme for solving Maxwell's equations in vacuum. The scheme belongs to the lattice Maxwell methods (LMM) class, which was developed from modern lattice Boltzmann methods (LBM) for fluid dynamics problems. The scheme differs fundamentally in construction from the finite difference time domain methods (FDTD) and is free of some problems of FDTD schemes. The components of the electric and magnetic fields are expressed as linear combinations of twelve variables that can be related to a spatially isotropic set of monochromatic plane waves. For the first time, the numerical dispersion of the scheme is investigated and an explicit one-to-one functional relationship between the variables of the numerical scheme and the electromagnetic fields is given.
