  In the famous textbook written by Landau and Lifshitz all the vacuum metrics
of the general theory of relativity are derived, which depend on one coordinate
in the absence of a cosmological constant. Unfortunately, when considering
these solutions, the authors missed some of the possible solutions discussed in
this article. An exact solution is demonstrated, which is absent in the book by
Landau and Lifshitz. It describes space-time with a gravitational wave of zero
frequency. It is shown that there are no other solutions of this type than
listed above and Minkowski's metrics. The list of vacuum metrics that depend on
one coordinate is not complete without the solution provided in this paper.
