The electrosurgical apparatus (10) comprises: a generator system (12) configured to generate a radio-frequency electric signal, and a handpiece (14) to be gripped by an operator and comprising an end (16) fitted with an active electrode (18) electrically connected to the generator system (12). The signal is capable of polarizing the active electrode (18) so as to generate a glow plasma discharge (19) in the atmosphere when the active electrode (18) is in the proximity of the tissue mass (M), without propagation of electric current through the patient's body (B).