  The hyperfine structure of atoms and ions is widely used in fundamental and
applied research. Accurate knowledge of hyperfine splitting values is essential
for quantum metrology applications as well as for improving the performance of
systems designed for quantum computing and simulation. We present refined
values of the hyperfine splitting frequencies of the ground and clock states of
thulium atom, $f_{g}^\textrm{HFS}=1\,496\,550\,658.23(3)$\,Hz and
$f_{c}^\textrm{HFS}=2\,113\,946\,873.08(9)$\,Hz, respectively. The measurements
are performed on an ultracold atomic ensemble in an optical lattice using
combined microwave and optical transition spectroscopy. Our results improve the
accuracy by 2 and 7 orders of magnitude for $f_{g}^\textrm{HFS}$ and
$f_{c}^\textrm{HFS}$, respectively, compared to the previously published
values. We also refine the value of the Land\'e g-factor of the clock level to
$g_c = 0.85479(11)$.
