A method for manufacturing a filtration membrane includes: a) selecting and preparing an organic polymer, such as a collodion; b) injecting a collodion into at least one channel of an extrusion die that also comprises an extrusion die core and at least one outlet; c) injecting an internal liquid into a hollow centering pin, the hollow centering pin comprising a channel positioned on the core of the extrusion die and also positioned at an axis of the outlet of the extrusion die; d) applying a holding film to the outlet of the extrusion die; e) unrolling the holding film onto a surface of at least one hollow fiber emerging from the outlet of the extrusion die; f) immersing the hollow fiber with the first holding film in a rinsing solution so as to obtain a flat hollow fiber filtration membrane; and ending the rinsing of the filtration membrane.