Skew-symmetric difference analogs of the fourth order of approximation of the first derivative

Let there be an initial boundary value problem for a system of first-order hyperbolic equations that has an integral conservation law. One of the options for the numerical solution of this kind of problem is the construction of a difference scheme for spatial variables, followed by the solution of the resulting system of ordinary differential equations.For the stability of the solution of this ODE system, it is desirable that it has the first integral, which is an analogue of the conservation law for the original problem. For this purpose, an antisymmetric difference analogue of the first derivative of the fourth order of approximation is constructed.