  Hydrogen recombination lines at the submillimetre band (submm-RLs) can serve
as probes of ionized gas without dust extinction. One therefore expects to
probe the broad line region (BLR) of an obscured (type 2) active galactic
nucleus (AGN) with those lines. However, admitting the large uncertainty in the
continuum level, here we report on the non-detection of both broad and narrow
H26$\alpha$ emission line (rest frequency = 353.62 GHz) towards the
prototypical type 2 AGN of NGC 1068 with the Atacama Large
Millimeter/submillimeter Array (ALMA). We also investigate the nature of BLR
clouds that can emit submm-RLs with model calculations. As a result, we suggest
that clouds with an electron density ($N_e$) of $\sim$ 10$^9$ cm$^{-3}$ can
mainly contribute to broad submm-RLs in terms of the line flux. On the other
hand, line flux from other density clouds would be insignificant considering
their too large or too small line optical depths. However, even for the case of
$N_e \sim 10^9$ cm$^{-3}$ clouds, we also suggest that the expected line flux
is extremely low, which is impractical to detect even with ALMA.
