  The molecular outflow from IRAS 04166+2706 was mapped with the Submillimeter
Array (SMA) at 350 GHz continuum and CO J = 3$-$2 at an angular resolution of
~1 arcsec. The field of view covers the central arc-minute, which contains the
inner four pairs of knots of the molecular jet. On the channel map, conical
structures are clearly present in the low velocity range (|V$-$V$_0$|$<$10 km
s$^{-1}$), and the highly collimated knots appear in the Extremely High
Velocity range (EHV, 50$>$|V$-$V$_0$|$>$30 km s$^{-1}$). The higher angular
resolution of ~1 arcsec reveals the first blue-shifted knot (B1) that was
missing in previous PdBI observation of Sant\'iago-Garc\'ia et al. (2009) at an
offset of ~6 arcsec to the North-East of the central source. This
identification completes the symmetric sequence of knots in both the blue- and
red-shifted lobes of the outflow. The innermost knots R1 and B1 have the
highest velocities within the sequence. Although the general features appear to
be similar to previous CO J = 2$-$1 images in Sant\'iago-Garc\'ia et al.
(2009), the emission in CO J = 3$-$2 almost always peaks further away from the
central source than that of CO J = 2$-$1 in the red-shifted lobe of the channel
maps. This gives rise to a gradient in the line-ratio map of CO J = 3$-$2/J =
2$-$1 from head to tail within a knot. A large velocity gradient (LVG) analysis
suggests that the differences may reflect a higher gas kinetic temperature at
the head. We also explore possible constraints imposed by the non-detection of
SiO J = 8$-$7.
