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An HI mass function (HIMF) was derived for 751 galaxies selected from the deep Parkes HI survey across the Zone of Avoidance (HIZOA). HIZOA contains both the Great Attractor Wall and the Local Void, two of the most extreme environments in the local Universe, making the sample eminently suitable to explore the overall HIMF as well as its dependence on local environment. To avoid any selection bias because of the different distances of these large-scale structures, we first used the 2D stepwise maximum-likelihood method for the definition of an average HIMF. The resulting parameters of a Schechter-type HIMF for the whole sample are α = -1.33 ± 0.05, log(MHI/Mθ) = 9.93 ± 0.04, and Φ= (3.9 ± 0.6) × 10-3 Mpc-3. We then used the k-th nearest-neighbour method to subdivide the sample into four environments of decreasing local density and derived the Schechter parameters for each subsample. A strong trend is observed, for the slope α of the low-mass end of the HIMF. The slope changes from being nearly flat, i.e. α = -0.99 ± 0.19 for galaxies residing in the densest bin, to the steep value of α = -1.31 ± 0.10 in the lowest density bin. The characteristic mass, however, does not show a clear trend between the highest and lowest density bins. We find similar trends in the low-mass slope when we compare the results for a region dominated by the Great Attractor, and the Local Void, which are found to be over-, respectively underdense by 1.35 and 0.59 compared to the whole sample.