  We report Swift Burst Alert Telescope (BAT) observations of the X-ray Flash
(XRF) XRF 050416A. The fluence ratio between the 15-25 keV and 25-50 keV energy
bands of this event is 1.5, thus making it the softest gamma-ray burst (GRB)
observed by BAT so far. The spectrum is well fitted by the Band function with
E^{\rm obs}_{\rm peak} of 15.0_{-2.7}^{+2.3} keV. Assuming the redshift of the
host galaxy (z = 0.6535), the isotropic-equivalent radiated energy E_{\rm iso}
and the peak energy at the GRB rest frame (E^{\rm src}_{\rm peak}) of XRF
050416A are not only consistent with the correlation found by Amati et al. and
extended to XRFs by Sakamoto et al., but also fill-in the gap of this relation
around the 30 - 80 keV range of E^{\rm src}_{\rm peak}. This result tightens
the validity of the E^{\rm src}_{\rm peak} - E_{\rm iso} relation from XRFs to
GRBs.
  We also find that the jet break time estimated using the empirical relation
between E^{\rm src}_{\rm peak} and the collimation corrected energy E_{\gamma}
is inconsistent with the afterglow observation by Swift X-ray Telescope. This
could be due to the extra external shock emission overlaid around the jet break
time or to the non existence of a jet break feature for XRF, which might be a
further challenging for GRB jet emission, models and XRF/GRB unification
scenarios.
