We present the results of radial velocity measurements of 770 thick disk red giants toward the South Galactic Pole, vertically distributed from 0.5 kpc to 5 kpc with respect to the Galactic plane. We find a small gradient, in the vertical velocity dispersion (sigma(W)) of 3.8 +/- 0.8 km s(-1) kpc(-1). Even more noteworthy, our values of sigma(W) are small compared to literature values: in the middle of the vertical height range we find sigma(W,z=2kpc)=30 km s(-1). We found no possible explanation for this small value of sigma(W) in terms of sample contamination by thin disk stars, nor by wrong assumptions regarding the metallicity distribution and the derived distances.