  We prove that there exists just one pair of complex four-dimensional Lie
algebras such that a well-defined contraction among them is not equivalent to a
generalized IW-contraction (or to a one-parametric subgroup degeneration in
conventional algebraic terms). Over the field of real numbers, this pair of
algebras is split into two pairs with the same contracted algebra. The example
we constructed demonstrates that even in the dimension four generalized
IW-contractions are not sufficient for realizing all possible contractions, and
this is the lowest dimension in which generalized IW-contractions are not
universal. Moreover, this is also the first example of nonexistence of
generalized IW-contraction for the case when the contracted algebra is not
characteristically nilpotent and, therefore, admits nontrivial diagonal
derivations. The lower bound (equal to three) of nonnegative integer parameter
exponents which are sufficient to realize all generalized IW-contractions of
four-dimensional Lie algebras is also found.
