Method of preparing a polyethylene glycol (pegylated) human growth hormone or a preparation of polyethylene glycol (pegylated) human growth hormone, comprising: (a) in a solution with a pH not less than 6.0, put the branched double stranded polyethylene glycol (PEG) U-shaped or Y-shaped in contact with human growth hormone； (b) evaluate the product modified by the double-stranded PEG at a single site obtained in step a) in SDS-PAGE of appropriate concentration, where the product shows two bands； (c) separating and recovering the product of lower apparent molecular weight in the two bands modified by the double-stranded PEG at a single site, where the U-branched double-stranded polyethylene glycol has the following formula (IV) ** Formula **, where , R and R 'are independently low molecular weight alkyl； n and n 'indicate the degree of polymerization and can be any integer； n + n 'is between 600 and 1500； The average molecular weight of the U-shaped branched PEG is approximately from 26kD to 66kD, or where the Y-branched double stranded polyethylene glycol has the following formula (III): ** Formula ** where, R and R 'are independently alkyl of low molecular weight, m and m 'indicate the degree of polymerization and can be any integer, j is an integer from 1 to 12, and the average total molecular weight of the Y-branched PEG is approximately 26kD to 60kD.Metodo de preparacion de una hormona de crecimiento humana polietilenglicolada (pegilada) o una preparacion de hormona de crecimiento humana polietilenglicolada (pegilada), que comprende: (a) en una solucion con pH no inferior a 6.0, poner el polietilenglicol (PEG) bicatenario ramificado con forma de U o con forma de Y en contacto con la hormona de crecimiento humana； (b) evaluar el producto modificado por el PEG bicatenario en un unico sitio obtenido en el paso a) en SDS-PAGE de concentracion apropiada, donde el producto muestra dos bandas； (c) separar y recuperar el producto de peso molecular aparente inferior en l
