  The total domination game is a two-person competitive optimization game,
where the players, Dominator and Staller, alternately select vertices of an
isolate-free graph $G$. Each vertex chosen must strictly increase the number of
vertices totally dominated. This process eventually produces a total dominating
set of $G$. Dominator wishes to minimize the number of vertices chosen in the
game, while Staller wishes to maximize it. The game total domination number of
$G$, $\gamma_{{\rm tg}}(G)$, is the number of vertices chosen when Dominator
starts the game and both players play optimally.
  Recently, Henning, Klav\v{z}ar, and Rall proved that $\gamma_{{\rm tg}}(G)
\le \frac{4}{5}n$ holds for every graph $G$ which is given on $n$ vertices such
that every component of it is of order at least $3$; they also conjectured that
the sharp upper bound would be $\frac{3}{4}n$. Here, we prove that
$\gamma_{{\rm tg}}(G)\le \frac{11}{14}n$ holds for every $G$ which contains no
isolated vertices or isolated edges.
