  We calculate the cosmic microwave background (CMB) angular trispectrum,
spherical harmonic transform of the four-point correlation function, from
primordial non-Gaussianity in primordial curvature perturbations characterized
by a constant non-linear coupling parameter, $f_{\rm NL}$. We fully take into
account the effect of the radiation transfer function, and thus provide the
most accurate estimate of the signal-to-noise ratio of the angular trispectrum
of CMB temperature anisotropy. We find that the predicted signal-to-noise ratio
of the trispectrum summed up to a given $l$ is approximately a power-law,
$(S/N)(<l)\sim 2.2\times 10^{-9}f^2_{\rm NL}l^2$, up to the maximum multipole
that we have reached in our numerical calculation, $l=1200$, assuming that the
error is dominated by cosmic variance. Our results indicate that the
signal-to-noise ratio of the temperature trispectrum exceeds that of the
bispectrum at the critical multipole, $l_c \sim 1500~(50/|f_{\rm NL}|)$.
Therefore, the trispectrum of the Planck data is more sensitive to primordial
non-Gaussianity than the bispectrum for $|f_{\rm NL}|\gtrsim 50$. We also
report the predicted constraints on the amplitude of trispectrum, which may be
useful for other non-Gaussian models such as curvaton models.
