  It is well know that the precise measurement of $H\to\gamma\gamma$ can
generate two degenerate parameter spaces of $H\gamma\gamma$ anomalous coupling.
We propose to utilize the exclusive Higgs rare decays $H\to\Upsilon(ns)+\gamma$
to break above mentioned degeneracy and further to constrain the
$H\gamma\gamma$ anomalous coupling at the HL-LHC. We demonstrate that the
branching ratios of $H\to\Upsilon(ns)+\gamma$ can be significantly enhanced in
the non-SM-like parameter space from $H\to\gamma\gamma$ measurement, due to the
destructive interference between the direct and indirect production of
$\Upsilon(ns)$ in the SM. By applying the NRQCD factorization formalism, we
calculate the partial decay widths of $H\to\Upsilon(ns)+\gamma$ at the NLO
accuracy of $\alpha_s$. We show that it is hopeful to break such degenerate
parameter space at the HL-LHC if we can further highly suppress the background
and enhance the signal efficiency compared to the ATLAS preliminary simulation.
