  We define a nontrivial version of the square principle $\Box_\omega$, which
we then show consistent by means of forcing with finite conditions.
  This paper has been withdrawn by the author due to the fact that the
presented $\Box_\omega$ can be constructed in ZFC, as shown by Lajos Soukup and
Philip Welch.
  Note, that the forcing itself has not been found flawed.
