  Adopting the Lindblom-Detweiler formalism for polar oscillations of neutron
stars, we study the $w$-mode oscillation and find that the Lagrangian change in
pressure, measured by the physical quantity $X$, is negligibly small. Based on
this observation, we develop the generalised inverse-Cowling approximation
(GICA) with the approximation $X=X'=0$, where $X'$ is the derivative of $X$
with respect to the circumferential radius, for $w$-mode oscillations of
neutron stars. Under GICA, $w$-mode oscillations are described by a
second-order differential system, which can yield accurate frequencies and
damping rates of quasi-normal modes.
