to hold the melt temperature of the polymer melt in a range above 300 u00b0 c preferably in a range between 300 and 400 u00b0 c then the polymer melt is extruded through the nozzle holes 5 to form a respective fiber strand 6 after the fiber strands 6 emerge from the nozzle holes 5 they arrive in the acceleration section 15 and are brought together with a blowing stream thus the fiber strands 6 and the blowing stream are accelerated continuously inside the acceleration section 15 as far as up to an exit throat in this way the fiber strands 6 are increasingly stretched the result is that following the expansion of the blowing stream in the free space said fiber strands form microfibers with a fiber cross section in a range between 0 5 u03bcm and 30 u03bcm then the microfibers 11 are deposited continuously as the non woven fabric 14 on the depositing belt 13 a cold blowing medium preferably cold air is used as the blowing medium for taking off and stretching the fiber strands 6 this process allows the fiber strands to cool down until they are deposited so that no additional cooling of the fibers is necessary at air temperatures of for example 25 u00b0 c in particular the free space 12 between the blower 3 and the depositing belt 13 can be held extremely small so that the blowing stream significantly improves the depositing of the microfibers so as to form a non woven fabric in addition the stability of the fiber guide is enhanced in that when the cold blowing air meets the freshly extruded fiber strands rapid cooling of the peripheral zones of the fiber strands 6 takes place however.