  The Parker instability is considered to play important roles in the evolution
of the interstellar medium. Most studies on the development of the instability
so far have been based on an initial equilibrium system with a uniform magnetic
field. However, the Galactic magnetic field possesses a random component in
addition to the mean uniform component, with comparable strength of the two
components. Parker and Jokipii have recently suggested that the random
component can suppress the growth of small wavelength perturbations. Here, we
extend their analysis by including gas pressure which was ignored in their
work, and study the stabilizing effect of the random component in the
interstellar gas with finite pressure. Following Parker and Jokipii, the
magnetic field is modeled as a mean azimuthal component, $B(z)$, plus a random
radial component, $\epsilon(z) B(z)$, where $\epsilon(z)$ is a random function
of height from the equatorial plane. We show that for the observationally
suggested values of $<\epsilon^2>^{1/2}$, the tension due to the random
component becomes important, so that the growth of the instability is either
significantly reduced or completely suppressed. When the instability still
works, the radial wavenumber of the most unstable mode is found to be zero.
That is, the instability is reduced to be effectively two-dimensional. We
discuss briefly the implications of our finding.
