For the first time, the possibility of maintaining an intact human mitochondrial genome in a heterologous system in the mitochondria of yeast Yarrowia lipolytica is shown. A method for introducing directional changes into the structure of the mitochondrial human genome replicating in Y. lipolytica by an artificially induced ability of yeast mitochondria for homologous recombination is proposed. A method of introducing and using phenotypic selection markers for the presence or absence of defects in genes tRNA-Lys and tRNA-Leu of the mitochondrial genome is developed. The proposed system can be used to correct harmful mutations of the human mitochondrial genome associated with mitochondrial diseases and for preparative amplification of intact mitochondrial DNA with an adjusted sequence in yeast cells. The applicability of the new system for the correction of mutations in the genes of Lys- and Leu-specific tRNAs of the human mitochondrial genome associated with serious and widespread human mitochondrial diseases such as myoclonic epilepsy with lactic acidosis (MELAS) and myoclonic epilepsy with ragged-red fibers (MERRF) is shown.