  We extend the work by S. Iso, H. Umetsu and F. Wilczek [Phys. Rev. Lett. 96
(2006) 151302] to derive the Hawking flux via gauge and gravitational anomalies
of a most general two-dimensional non-extremal black hole space-time with the
determinant of its diagonal metric differing from the unity ($\sqrt{-g} \neq
1$) and use it to investigate Hawking radiation from the Reissner-Nordstrom
black hole with a global monopole by requiring the cancellation of anomalies at
the horizon. It is shown that the compensating energy momentum and gauge fluxes
required to cancel gravitational and gauge anomalies at the horizon are
precisely equivalent to the $(1+1)$-dimensional thermal fluxes associated with
Hawking radiation emanating from the horizon at the Hawking temperature. These
fluxes are universally determined by the value of anomalies at the horizon.
