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The High Energy Stereoscopic System (H.E.S.S.) is an array of five imaging atmospheric Cherenkov telescopes located in the Khomas Highland of Namibia. H.E.S.S. operates in a wide energy range from several tens of GeV to several tens of TeV, reaching the best sensitivity around 1 TeV or at lower energies. However, there are many important topics – such as the search for Galactic PeVatrons, the study of gamma-ray production scenarios for sources (hadronic vs. leptonic), EBL absorption studies – which require good sensitivity at energies above 10 TeV. This work aims at improving the sensitivity of H.E.S.S. and increasing the gamma-ray statistics at high energies. The study investigates an enlargement of the H.E.S.S. effective field of view using events with larger offset angles in the analysis. The greatest challenges in the analysis of large-offset events are a degradation of the reconstruction accuracy and a rise of the background rate as the offset angle increases. The more sophisticated direction reconstruction method (DISP) and improvements to the standard background rejection technique, which by themselves are effective ways to increase the gamma-ray statistics and improve the sensitivity of the analysis, are implemented to overcome the above-mentioned issues. As a result, the angular resolution at the preselection level is improved by 5 - 10% for events at 0.5◦ offset angle and by 20 - 30% for events at 2◦ offset angle. The background rate at large offset angles is decreased nearly to a level typical for offset angles below 2.5◦. Thereby, sensitivity improvements of 10 - 20% are achieved for the proposed analysis compared to the standard analysis at small offset angles. Developed analysis also allows for the usage of events at large offset angles up to approximately 4◦, which was not possible before. This analysis method is applied to the analysis of the Galactic plane data above 10 TeV. As a result, 40 sources out of the 78 presented in the H.E.S.S. Galactic plane survey (HGPS) are detected above 10 TeV. Among them are representatives of all source classes that are present in the HGPS catalogue; namely, binary systems, supernova remnants, pulsar wind nebulae and composite objects. The potential of the improved analysis method is demonstrated by investigating the more than 10 TeV emission for two objects: the region associated with the shell-type SNR HESS J1731−347 and the PWN candidate associated with PSR J0855−4644 that is coincident with Vela Junior (HESS J0852−463).