The invention provides a method of detecting partial discharges in an electrical appliance insulated in a receptacle and a system of diagnosing the state of the appliance using this method. With the help of an UHF antenna placed in the receptacle of the appliance, the method includes analyzing the spectrum (RS1) of the electromagnetic signal picked up by the antenna and of identifying within the spectrum one or more frequencies of interest (B1, B2), for each of which the signal has an amplitude greater than a predetermined threshold value. To identify the frequency/frequencies of interest, the spectrum of the signal received by the antenna is compared with a reference spectrum (RS2).