[en] A scalar wave equation is considered on the background of some Bianchi-type I universe with regard to which its time-symmetric Green's function can be obtained exactly. The explicitly known Green's function constituents are expanded up to a certain order of a parameter epsilon marking the deviations of the Bianchi-type metric from the Minkowski metric. The result is seen to coincide with that one obtained by calculating the Green's function constituents for the special Bianchi-type I metric via general approximation formulae derived earlier by a Lorentz-invariant perturbational method. (author)