The results obtained in a study of the synthesis of n⁺-GaN layers by plasma-assisted molecular-beam epitaxy on GaN/c-Al₂O₃ templates are reported. In particular, a method is developed for the pre-epitaxial cleaning of the GaN surfaces of templates to remove foreign atoms. It is shown that, to form GaN layers of comparatively good quality, including those doped with silicon up to ~4.6 × 10¹⁹ cm^–3, GaN template surfaces should be pre-epitaxially cleaned in a flow of activated nitrogen particles, with the substrate temperature increased from T_S = 400 to 600°C and the substrate surface subsequently exposed to a flow of activated nitrogen at a fixed value of T_S = 600°C for 1 h. After that the substrate temperature should be raised to T_S = 700°C and the GaN surface finally cleaned by means of a procedure for gallium deposition/desorption.