We investigate a diagonal Riemannian metric. The metric represented by four unknown functions, two of them depend on $x^1$ only and two depend on $x^4$ only. We compose the Einstein tensor. The functions composing the metric tensor are determined from tho condition that the form of Einstein tensor correspond to the energy-momentum tensor of the pure radiation field. This is the special case of the electromagnetic field for which the electric and magnetic three-vectors are equal and perpendicular.