<p>We present a new implementation of the numerical scheme for solving Maxwell’s differential equations in vacuum. In its structure, the scheme is fundamentally different from the finite-difference time-domain methods and is free of some of the problems inherent in such 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. The dispersion of the scheme is investigated for the first time, and an explicit and one-to-one functional relationship between the variables of the numerical scheme and the electromagnetic fields is presented. The results are demonstrated using the example of simulating plane waves and a focused laser pulse.</p>