We find solid evidence for diffuse HI gas at substantial z heights in
our Galaxy, with a velocity dispersion of sigma = 60 km s(-1) and a ve
rtical projected column density of N-Hi = 1.4 . 10(19) cm(-2). This pe
rvasive component of the emission spectrum could be identified in the
Leiden/Dwingeloo 21-cm Survey (LDS) after increasing the accuracy furt
her by correcting the observations for reflections from the ground. In
vestigations of receiver bandpass and stray radiation effects could no
t explain this component as an artifact of the instrumentation. Assumi
ng that the distribution of mass and pressure perpendicular to the gal
actic plane is in hydrostatic equilibrium with the galactic potential,
we derive a vertical exponential scale height of h(z) similar or equa
l to 4.4 kpc for the observed diffuse high-dispersion HI component. Th
e radial distribution is characterized by the corresponding galactocen
tric scale length A(1) similar or equal to 15 kpc.