  For a simple digraph $G$ without directed triangles or digons, let $\beta(G)$
be the size of the smallest subset $X \subseteq E(G)$ such that $G\setminus X$
has no directed cycles, and let $\gamma(G)$ be the number of unordered pairs of
nonadjacent vertices in $G$. In 2008, Chudnovsky, Seymour, and Sullivan showed
that $\beta (G) \le \gamma(G)$, and conjectured that $\beta (G) \le
\gamma(G)/2$. Recently, Dunkum, Hamburger, and P\'or proved that $\beta (G) \le
0.88 \gamma(G)$. In this note, we prove that $\beta (G) \le 0.8616 \gamma(G)$.
