  We show that injective isometries in Orlicz space $L_M$ have to preserve
disjointness, provided that Orlicz function $M$ satisfies $\Delta_2$-condition,
has a continuous second derivative $M''$, satisfies another ``smoothness type''
condition and either
  $\lim_{t\to0} M''(t) = \infty$ or $M''(0) = 0$ and $M''(t)>0$ for all $t>0$.
The fact that surjective isometries of any rearrangement-invariant function
space have to preserve disjointness has been determined before. However
dropping the assumption of surjectivity invalidates the general method. In this
paper we use a differential technique.
