We use observations of the neutral atomic hydrogen (HI) 21-cm emission line to study the spatial distribution of the HI gas in a 80° × 90° region of the Galaxy halo. The HI column densities in the range of 3–11 × 10 20 cm − 2 have been estimated for some of the studied regions. In our map—obtained with a spectral sensitivity of ∼2 K—we do not detect any HI 21-cm emission line above 2 σ at Galactic latitudes higher than ∼46°. This report summarizes our contribution presented at the conference on the origin and evolution of barionic Galaxy halos.