  In this paper, we propose an extension of the Ricci-inverse gravity, which
has been proposed recently as a very novel type of fourth-order gravity, by
introducing a second order term of the so-called anticurvature scalar as a
correction. The main purpose of this paper is that we would like to see whether
the extended Ricci-inverse gravity model admits the homogeneous and isotropic
Friedmann-Lemaitre-Robertson-Walker metric as its stable inflationary solution.
However, a no-go theorem for inflation in this extended Ricci-inverse gravity
is shown to appear through a stability analysis based on the dynamical system
method. As a result, this no-go theorem implies that it is impossible to have
such stable inflation in this extended Ricci-inverse gravity model.
