  A complete mapping in the Brillouin zone of the structural instability
associated with the ferroelectric phase transitions of KNbO$_3$ has been
obtained by first-principles calculations using an LAPW linear response
approach. The wavevector dependence of the instability reveals pronounced
two-dimensional character, which corresponds to chains oriented along
$\left<100\right>$\ directions of displaced Nb atoms. The results are discussed
in relation to models of the ferroelectric phase transitions.
