We studied the complete randomness of the angular distribution of BATSE gamma-ray bursts (GRBs). Based on their durations and peak fluxes, we divided the BATSE sample into 5 subsamples (short1, short2, intermediate, long1, long2) and studied the angular distributions separately. We used three methods to search for non-randomness in the subsamples: Voronoi tesselation, minimal spanning tree, and multifractal spectra. To study any non-randomness in the subsamples we defined 13 test-variables (9 from Voronoi tesselation, 3 from the minimal spanning tree and one from the multifractal spectrum). We made Monte Carlo simulations taking into account the BATSE’s sky-exposure function. We tested therandomness by introducing squared Euclidean distances in the parameter space of the test-variables. We recognized that the short1, short2 groups deviate significantly (99.90%, 99.98%) from the fully random case in the distribution of the squared Euclidean distances but this is not true for the long samples. In the intermediate group, the squared Euclidean distances also give significant deviation (98.51%).