  Traditionally, it was accepted that a relational database can be normalized
step-by-step, from a set of un-normalized tables to tables in $1NF$, then to
$2NF$, then to $3NF$, then (possibly) to $BCNF$. The rule applied to a table in
$1NF$ in order to transform it to a set of tables in $2NF$ seems to be too
straightforward to pose any difficulty.
  However, we show that, depending on the set of functional dependencies, it is
impossible to reach $2NF$ and stop there; one must, in these cases, perform the
normalization from $1NF$ to $3NF$ as an indecomposable move. The minimal setup
to exhibit the phenomena requires a single composite key, and two partially
overlapping chains of transitive dependencies.
