  We revisit the fully online matching model (Huang et al., J.\ ACM, 2020), an
extension of the classic online matching model due to Karp, Vazirani, and
Vazirani (STOC 1990), which has recently received a lot of attention (Huang et
al., SODA 2019 and FOCS 2020), partly due to applications in ride-sharing
platforms. It has been shown that the fully online version is harder than the
classic version for which the achievable competitive ratio is at most $0.6317$,
rather than precisely $1-\frac{1}{e}\approx 0.6321$. We introduce two new ideas
to the construction. By optimizing the parameters of the modified construction
numerically, we obtain an improved impossibility result of $0.6297$. Like the
previous bound, the new bound even holds for fractional (rather than
randomized) algorithms on bipartite graphs.
