  We consider large time behavior of solutions to the nonlinear Schr\"odinger
equation with a homogeneous nonlinearity of the critical order which is not
necessarily a polynomial. We treat the case in which the nonlinearity contains
non-oscillating factor $|u|^{1+2/d}$. The case is excluded in our previous
studies. It turns out that there are no solutions that behave like a free
solution with or without logarithmic phase corrections. We also prove
nonexistence of an asymptotic free solution in the case that the gauge
invariant nonlinearity is dominant, and give a finite time blow-up result.
