  In the paper the spectral temporal evolution of a steeply rising
submillimeter (THz) burst occurred on 2003 November 2 was investigated in
detail for the first time. Observations show that the flux density of the THz
spectrum increased steeply with frequency above 200 GHz. Their average rising
rates reached a value of 235 sfu/GHz (corresponding spectral index $\alpha$ of
4.8) during the burst. The flux densities reached about 4,000 and 70,000 sfu at
212 and 405 GHz at maximum phase, respectively. The emissions at 405 GHz
maintained continuous high level that they exceed largely the peak values of
the microwave (MW) spectra during the main phase. Our studies suggest that only
energetic electrons with a low-energy cutoff of $\sim$1 MeV and number density
of $\sim$$10^{6}$--$10^{8}$ cm$^{-3}$ can produce such strong and steeply
rising THz component via gyrosynchrotron (GS) radiation based on numerical
simulations of burst spectra in the nonuniform magnetic field case. The
electron number density $N$, derived from our numerical fits to the THz
temporal evolution spectra, increased substantially from $8\times10^{6}$ to
$4\times10^{8}$ cm$^{-3}$, i.e., $N$ value increased 50 times during the rise
phase. During the decay phase it decreased to $7\times10^{7}$ cm$^{-3}$, i.e.,
decreased about five times from the maximum phase. The total electron number
decreased an order of magnitude from the maximum phase to the decay phase.
Nevertheless the variation amplitude of $N$ is only about one time in the MW
emission source during this burst, and the total electron number did not
decrease but increased by about 20$\%$ during the decay phase. Interestingly,
we find that the THz source radius decreased by about 24$\%$ while the MW
source one, on the contrary, increased by 28$\%$ during the decay phase.
