To let the water pass quickly through the ground coffee layer at a temperature below 100°C, the water is heated to the desired temperature and is then vacuum drawn through the powdered coffee, the vacuum being generated by steam cooling and condensation. A coffee machine, consisting of an upper vessel (2) which can be tightly connected to a lower vessel (1) with the interposition of a coffee filter basket (4) is fitted with a rising transfer tube (9) extending from just above the bottom of the lower vessel (1) upwards to the upper vessel (2) and with a shut-off valve (13) which opens in direction of the upper vessel (2), while this upper vessel (2) is communicating by means of a siphon (19, 20) with the coffee filter basket (4) which, in turn, is at its lower end connected to the lower vessel (1) by means of a non-return valve (17, 18) that can be opened in direction of the lower vessel (1).