The method comprises the following steps: the printed circuit board is provided with an insulating layer, (with the exception of the contact surfaces); contact bumps or contact layers with a maximum height of 100 νm, consisting of a solder material with a good thermal conductivity, are either applied to one surface of the contact electrodes of the LED dice, or contact layers with a thickness of 1-50 νm are applied to the contact surfaces of the printed circuit board; the LED dice are pressed and soldered onto the contact surfaces of the printed circuit board, or in their immediate vicinity, using flip-chip technology, the contact surface of said dice facing downwards. Said method can be modified so that instead of the soldering process, metallic contact bumps or contact layers are used and the LED dice are pressed in exact register onto the free contact surfaces of the printed circuit board and are fixed using a thermocompression procedure. Said method can also be modified for LEDs comprising contacts on their front faces. The method permits the production of LED arrays with an intense luminosity, despite their reduced dimensions.