  We numerically study the SU(2)$\otimes$SU(2) symmetric spin-orbit coupled
model as a lower symmetric generalization of the SU(4) exchange model. On the
symmetric line with respect to the spin and orbit, our result shows the
essentially singular gap formation in consistent with the analytic approach,
which is different from the previous numerical calculation. Furthermore, we
find new critical phases around the SU(4) point, surrounding the previously
known gapless symmetric line. In these novel phases either spin or orbital
excitations around momentum $q=\pi$ form massless continua which split from the
excitations belonging to the $[2^2]$ irreducible representation at the SU(4)
point. On the critical symmetric line, the additional coupled spin-orbit
excitations around $q=\pi/2$ originating from [$2^11^2$] become critical, too.
